Practice · A sunk object's volume is the water it pushes up · Sensim Math

Variant 1 easy

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $18\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 16 cm by 14 cm holds water 12 cm deep. A stone goes in, fully under, and the water reaches 18 cm. We want the stone's volume.

Givens

The tank's base is 16 cm by 14 cm.
The water starts 12 cm deep and ends 18 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

18 - 12 = 6

The water climbed 6 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 16 by 14 base, 6 cm thick.

16 \times 14 \times 6 = 1344

The stone is 1344 cm3.

Answer: 1344 cm³

4 · Reviewdoes it hold up?

The water before was 2688 cm3 and after is 4032 cm3; the difference, 1344 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 4032 minus 2688, the same 1344 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 2 easy

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $20\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 18 cm by 12 cm holds water 15 cm deep. A stone goes in, fully under, and the water reaches 20 cm. We want the stone's volume.

Givens

The tank's base is 18 cm by 12 cm.
The water starts 15 cm deep and ends 20 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

20 - 15 = 5

The water climbed 5 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 18 by 12 base, 5 cm thick.

18 \times 12 \times 5 = 1080

The stone is 1080 cm3.

Answer: 1080 cm³

4 · Reviewdoes it hold up?

The water before was 3240 cm3 and after is 4320 cm3; the difference, 1080 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 4320 minus 3240, the same 1080 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 3 easy

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $21\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 24 cm by 18 cm holds water 16 cm deep. A stone goes in, fully under, and the water reaches 21 cm. We want the stone's volume.

Givens

The tank's base is 24 cm by 18 cm.
The water starts 16 cm deep and ends 21 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

21 - 16 = 5

The water climbed 5 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 24 by 18 base, 5 cm thick.

24 \times 18 \times 5 = 2160

The stone is 2160 cm3.

Answer: 2160 cm³

4 · Reviewdoes it hold up?

The water before was 6912 cm3 and after is 9072 cm3; the difference, 2160 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 9072 minus 6912, the same 2160 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 4 easy

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $24\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 25 cm by 15 cm holds water 20 cm deep. A stone goes in, fully under, and the water reaches 24 cm. We want the stone's volume.

Givens

The tank's base is 25 cm by 15 cm.
The water starts 20 cm deep and ends 24 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

24 - 20 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 25 by 15 base, 4 cm thick.

25 \times 15 \times 4 = 1500

The stone is 1500 cm3.

Answer: 1500 cm³

4 · Reviewdoes it hold up?

The water before was 7500 cm3 and after is 9000 cm3; the difference, 1500 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 9000 minus 7500, the same 1500 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 5 medium

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $26\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 28 cm by 20 cm holds water 22 cm deep. A stone goes in, fully under, and the water reaches 26 cm. We want the stone's volume.

Givens

The tank's base is 28 cm by 20 cm.
The water starts 22 cm deep and ends 26 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

26 - 22 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 28 by 20 base, 4 cm thick.

28 \times 20 \times 4 = 2240

The stone is 2240 cm3.

Answer: 2240 cm³

4 · Reviewdoes it hold up?

The water before was 12320 cm3 and after is 14560 cm3; the difference, 2240 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 14560 minus 12320, the same 2240 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 6 medium

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $22\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 30 cm by 20 cm holds water 18 cm deep. A stone goes in, fully under, and the water reaches 22 cm. We want the stone's volume.

Givens

The tank's base is 30 cm by 20 cm.
The water starts 18 cm deep and ends 22 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

22 - 18 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 30 by 20 base, 4 cm thick.

30 \times 20 \times 4 = 2400

The stone is 2400 cm3.

Answer: 2400 cm³

4 · Reviewdoes it hold up?

The water before was 10800 cm3 and after is 13200 cm3; the difference, 2400 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 13200 minus 10800, the same 2400 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 7 medium

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $30\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 20 cm by 16 cm holds water 25 cm deep. A stone goes in, fully under, and the water reaches 30 cm. We want the stone's volume.

Givens

The tank's base is 20 cm by 16 cm.
The water starts 25 cm deep and ends 30 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

30 - 25 = 5

The water climbed 5 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 20 by 16 base, 5 cm thick.

20 \times 16 \times 5 = 1600

The stone is 1600 cm3.

Answer: 1600 cm³

4 · Reviewdoes it hold up?

The water before was 8000 cm3 and after is 9600 cm3; the difference, 1600 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 9600 minus 8000, the same 1600 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 8 medium

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $30\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 22 cm by 18 cm holds water 26 cm deep. A stone goes in, fully under, and the water reaches 30 cm. We want the stone's volume.

Givens

The tank's base is 22 cm by 18 cm.
The water starts 26 cm deep and ends 30 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

30 - 26 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 22 by 18 base, 4 cm thick.

22 \times 18 \times 4 = 1584

The stone is 1584 cm3.

Answer: 1584 cm³

4 · Reviewdoes it hold up?

The water before was 10296 cm3 and after is 11880 cm3; the difference, 1584 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 11880 minus 10296, the same 1584 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 9 hard

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $28\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 35 cm by 22 cm holds water 24 cm deep. A stone goes in, fully under, and the water reaches 28 cm. We want the stone's volume.

Givens

The tank's base is 35 cm by 22 cm.
The water starts 24 cm deep and ends 28 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

28 - 24 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 35 by 22 base, 4 cm thick.

35 \times 22 \times 4 = 3080

The stone is 3080 cm3.

Answer: 3080 cm³

4 · Reviewdoes it hold up?

The water before was 18480 cm3 and after is 21560 cm3; the difference, 3080 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 21560 minus 18480, the same 3080 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 10 hard

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $33\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 40 cm by 25 cm holds water 30 cm deep. A stone goes in, fully under, and the water reaches 33 cm. We want the stone's volume.

Givens

The tank's base is 40 cm by 25 cm.
The water starts 30 cm deep and ends 33 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

33 - 30 = 3

The water climbed 3 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 40 by 25 base, 3 cm thick.

40 \times 25 \times 3 = 3000

The stone is 3000 cm3.

Answer: 3000 cm³

4 · Reviewdoes it hold up?

The water before was 30000 cm3 and after is 33000 cm3; the difference, 3000 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 33000 minus 30000, the same 3000 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 11 hard

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $38\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 45 cm by 28 cm holds water 35 cm deep. A stone goes in, fully under, and the water reaches 38 cm. We want the stone's volume.

Givens

The tank's base is 45 cm by 28 cm.
The water starts 35 cm deep and ends 38 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

38 - 35 = 3

The water climbed 3 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 45 by 28 base, 3 cm thick.

45 \times 28 \times 3 = 3780

The stone is 3780 cm3.

Answer: 3780 cm³

4 · Reviewdoes it hold up?

The water before was 44100 cm3 and after is 47880 cm3; the difference, 3780 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 47880 minus 44100, the same 3780 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

Variant 12 hard

A tank shaped like a rectangular prism holds water, as shown at the right. When a stone is placed in it so that the stone is completely under water, the water rises to a height of $44\ \text{cm}$ . What is the volume of the stone, in $\text{cm}^3$ ? (Ignore the thickness of the tank.)

Your answer

Show solution

1 · Understandwhat's really being asked

A tank 50 cm by 30 cm holds water 40 cm deep. A stone goes in, fully under, and the water reaches 44 cm. We want the stone's volume.

Givens

The tank's base is 50 cm by 30 cm.
The water starts 40 cm deep and ends 44 cm deep.
The stone is completely under water.

Unknowns

The volume of the stone.

Constraints

No water is added or spilled, and the stone's shape is never given.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#16 Count the Complement

The stone cannot be measured -- no shape is given. It does not need to be: the water it pushed out of the way has the same volume, and that water is a plain slab with the tank's base and the rise as its height.

3 · Execute3 carry out the plan

1Find how far the water rose

#7 Identify Subproblems 6.G.A.2

The difference between the two levels.

44 - 40 = 4

The water climbed 4 cm.

2See what that rise is made of

#16 Count the Complement 6.G.A.2

The stone took up room at the bottom, so the same amount of water had to go somewhere: straight up.

\text{stone} = \text{water pushed up}

Volume in equals volume up.

3Measure that slab of water

#17 Visualize Spatial Relationships 6.G.A.2

It fills the tank's whole 50 by 30 base, 4 cm thick.

50 \times 30 \times 4 = 6000

The stone is 6000 cm3.

Answer: 6000 cm³

4 · Reviewdoes it hold up?

The water before was 60000 cm3 and after is 66000 cm3; the difference, 6000 cm3, is exactly the space the stone is taking up.

Another way: Working with the two totals rather than the rise gives 66000 minus 60000, the same 6000 cm3 with larger numbers.

Standardsmin grade 6

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the displaced water as a rectangular prism.

💡Takeaway. You do not need a shape to measure a thing. If it goes under water, the water tells you how big it is.

A sunk object's volume is the water it pushes up · 12 practice problems

Generated variants — 12

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