← Volume is base area times height, whatever shape the base is · Surface Area and Volume of Solids

Volume is base area times height, whatever shape the base is · 12 practice problems

6.G.A.27.G.B.6

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 840 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 15 cm by 8 cm by 14 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 15 cm long, 8 cm deep and 14 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

15 \times 8 = 120

The floor is 120 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

120 \div 2 = 60

The base is 60 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

60 \times 14 = 840

The shaded solid is 840 cm3.

Answer: 840 cm³

4 · Reviewdoes it hold up?

The whole box is 1680 cm3 and the shaded solid is 840 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 840 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 2 easy answer: 1248 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 13 cm by 12 cm by 16 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 13 cm long, 12 cm deep and 16 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

13 \times 12 = 156

The floor is 156 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

156 \div 2 = 78

The base is 78 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

78 \times 16 = 1248

The shaded solid is 1248 cm3.

Answer: 1248 cm³

4 · Reviewdoes it hold up?

The whole box is 2496 cm3 and the shaded solid is 1248 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1248 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 3 easy answer: 1080 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 12 cm by 9 cm by 20 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 12 cm long, 9 cm deep and 20 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

12 \times 9 = 108

The floor is 108 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

108 \div 2 = 54

The base is 54 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

54 \times 20 = 1080

The shaded solid is 1080 cm3.

Answer: 1080 cm³

4 · Reviewdoes it hold up?

The whole box is 2160 cm3 and the shaded solid is 1080 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1080 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 4 easy answer: 1980 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 20 cm by 11 cm by 18 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 20 cm long, 11 cm deep and 18 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

20 \times 11 = 220

The floor is 220 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

220 \div 2 = 110

The base is 110 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

110 \times 18 = 1980

The shaded solid is 1980 cm3.

Answer: 1980 cm³

4 · Reviewdoes it hold up?

The whole box is 3960 cm3 and the shaded solid is 1980 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1980 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 5 medium answer: 840 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 16 cm by 5 cm by 21 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 16 cm long, 5 cm deep and 21 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

16 \times 5 = 80

The floor is 80 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

80 \div 2 = 40

The base is 40 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

40 \times 21 = 840

The shaded solid is 840 cm3.

Answer: 840 cm³

4 · Reviewdoes it hold up?

The whole box is 1680 cm3 and the shaded solid is 840 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 840 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 6 medium answer: 1540 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 22 cm by 14 cm by 10 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 22 cm long, 14 cm deep and 10 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

22 \times 14 = 308

The floor is 308 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

308 \div 2 = 154

The base is 154 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

154 \times 10 = 1540

The shaded solid is 1540 cm3.

Answer: 1540 cm³

4 · Reviewdoes it hold up?

The whole box is 3080 cm3 and the shaded solid is 1540 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1540 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 7 medium answer: 2040 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 17 cm by 10 cm by 24 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 17 cm long, 10 cm deep and 24 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

17 \times 10 = 170

The floor is 170 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

170 \div 2 = 85

The base is 85 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

85 \times 24 = 2040

The shaded solid is 2040 cm3.

Answer: 2040 cm³

4 · Reviewdoes it hold up?

The whole box is 4080 cm3 and the shaded solid is 2040 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 2040 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 8 medium answer: 675 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 9 cm by 6 cm by 25 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 9 cm long, 6 cm deep and 25 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

9 \times 6 = 54

The floor is 54 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

54 \div 2 = 27

The base is 27 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

27 \times 25 = 675

The shaded solid is 675 cm3.

Answer: 675 cm³

4 · Reviewdoes it hold up?

The whole box is 1350 cm3 and the shaded solid is 675 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 675 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 9 hard answer: 1800 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 25 cm by 18 cm by 8 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 25 cm long, 18 cm deep and 8 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

25 \times 18 = 450

The floor is 450 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

450 \div 2 = 225

The base is 225 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

225 \times 8 = 1800

The shaded solid is 1800 cm3.

Answer: 1800 cm³

4 · Reviewdoes it hold up?

The whole box is 3600 cm3 and the shaded solid is 1800 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1800 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 10 hard answer: 1260 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 28 cm by 15 cm by 6 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 28 cm long, 15 cm deep and 6 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

28 \times 15 = 420

The floor is 420 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

420 \div 2 = 210

The base is 210 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

210 \times 6 = 1260

The shaded solid is 1260 cm3.

Answer: 1260 cm³

4 · Reviewdoes it hold up?

The whole box is 2520 cm3 and the shaded solid is 1260 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1260 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 11 hard answer: 1260 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 30 cm by 7 cm by 12 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 30 cm long, 7 cm deep and 12 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

30 \times 7 = 210

The floor is 210 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

210 \div 2 = 105

The base is 105 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

105 \times 12 = 1260

The shaded solid is 1260 cm3.

Answer: 1260 cm³

4 · Reviewdoes it hold up?

The whole box is 2520 cm3 and the shaded solid is 1260 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 1260 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.

Variant 12 hard answer: 660 cm³

What is the volume of the shaded solid inside the rectangular prism at the right, in $\text{cm}^3$ ?

Show solution

1 · Understandwhat's really being asked

Inside a box 11 cm by 4 cm by 30 cm sits a prism with a triangular base, reaching the full height. We want the shaded prism's volume.

Givens

The box is 11 cm long, 4 cm deep and 30 cm tall.
The shaded solid's base is a triangle on the box's floor.
The shaded solid reaches the box's full height.

Unknowns

The volume of the shaded solid.

Constraints

The shaded solid is a prism: the same triangle at every height.

2 · Planchoose the strategy

#17 Visualize Spatial Relationships · also uses: #7 Identify Subproblems#9 Solve an Easier Related Problem

Length times width times height belongs to boxes, and this is not one. Base area times height belongs to every prism, so measure the triangle on the floor and raise it.

3 · Execute3 carry out the plan

1Measure the box's floor

#7 Identify Subproblems 6.G.A.2

The triangle is drawn on it, so start there.

11 \times 4 = 44

The floor is 44 cm2.

2Halve it for the triangle

#9 Solve an Easier Related Problem 6.G.A.2

The triangle is the floor cut along a diagonal, so it is exactly half.

44 \div 2 = 22

The base is 22 cm2.

3Raise it to the full height

#17 Visualize Spatial Relationships 7.G.B.6

The same triangle sits at every level, so volume is base times height.

22 \times 30 = 660

The shaded solid is 660 cm3.

Answer: 660 cm³

4 · Reviewdoes it hold up?

The whole box is 1320 cm3 and the shaded solid is 660 -- exactly half, which is what cutting the floor along a diagonal must give.

Another way: Cutting the box in two along that diagonal and taking either piece gives the same 660 cm3 without any formula at all.

Standardsmin grade 7

6.G.A.2 Volume of right rectangular prisms with fractional edges — Measuring the box's floor and halving it.
7.G.B.6 Solve real-world problems involving area, surface area, and volume — Using base area times height for a non-rectangular prism.

💡Takeaway. Every straight solid is its base area times its height. Only boxes get to use three edges.