Practice · Split the surface into the part the unknown touches and the part it does not · Sensim Math

Variant 1 easy

The cylinder at the right has a surface area of $188.4\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 3 cm has a surface area of 188.4 cm2. We want its height.

Givens

The base radius is 3 cm.
The surface area is 188.4 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 3 cm, whatever the height.

3 \times 3 \times 3.14 \times 2 = 56.52

56.52 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

188.4 - 56.52 = 131.88

131.88 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 18.84 cm.

3 \times 2 \times 3.14 = 18.84

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

131.88 \div 18.84 = 7

The cylinder is 7 cm tall.

Answer: 7 cm

4 · Reviewdoes it hold up?

Building it back up: 56.52 for the two bases plus 18.84 times 7 for the side comes to 188.4 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 2 easy

The cylinder at the right has a surface area of $326.56\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 4 cm has a surface area of 326.56 cm2. We want its height.

Givens

The base radius is 4 cm.
The surface area is 326.56 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 4 cm, whatever the height.

4 \times 4 \times 3.14 \times 2 = 100.48

100.48 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

326.56 - 100.48 = 226.08

226.08 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 25.12 cm.

4 \times 2 \times 3.14 = 25.12

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

226.08 \div 25.12 = 9

The cylinder is 9 cm tall.

Answer: 9 cm

4 · Reviewdoes it hold up?

Building it back up: 100.48 for the two bases plus 25.12 times 9 for the side comes to 326.56 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 3 easy

The cylinder at the right has a surface area of $527.52\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 6 cm has a surface area of 527.52 cm2. We want its height.

Givens

The base radius is 6 cm.
The surface area is 527.52 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 6 cm, whatever the height.

6 \times 6 \times 3.14 \times 2 = 226.08

226.08 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

527.52 - 226.08 = 301.44

301.44 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 37.68 cm.

6 \times 2 \times 3.14 = 37.68

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

301.44 \div 37.68 = 8

The cylinder is 8 cm tall.

Answer: 8 cm

4 · Reviewdoes it hold up?

Building it back up: 226.08 for the two bases plus 37.68 times 8 for the side comes to 527.52 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 4 easy

The cylinder at the right has a surface area of $533.8\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 5 cm has a surface area of 533.8 cm2. We want its height.

Givens

The base radius is 5 cm.
The surface area is 533.8 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 5 cm, whatever the height.

5 \times 5 \times 3.14 \times 2 = 157

157 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

533.8 - 157 = 376.8

376.8 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 31.4 cm.

5 \times 2 \times 3.14 = 31.4

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

376.8 \div 31.4 = 12

The cylinder is 12 cm tall.

Answer: 12 cm

4 · Reviewdoes it hold up?

Building it back up: 157 for the two bases plus 31.4 times 12 for the side comes to 533.8 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 5 medium

The cylinder at the right has a surface area of $1130.4\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 9 cm has a surface area of 1130.4 cm2. We want its height.

Givens

The base radius is 9 cm.
The surface area is 1130.4 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 9 cm, whatever the height.

9 \times 9 \times 3.14 \times 2 = 508.68

508.68 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

1130.4 - 508.68 = 621.72

621.72 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 56.52 cm.

9 \times 2 \times 3.14 = 56.52

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

621.72 \div 56.52 = 11

The cylinder is 11 cm tall.

Answer: 11 cm

4 · Reviewdoes it hold up?

Building it back up: 508.68 for the two bases plus 56.52 times 11 for the side comes to 1130.4 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 6 medium

The cylinder at the right has a surface area of $1186.92\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 7 cm has a surface area of 1186.92 cm2. We want its height.

Givens

The base radius is 7 cm.
The surface area is 1186.92 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 7 cm, whatever the height.

7 \times 7 \times 3.14 \times 2 = 307.72

307.72 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

1186.92 - 307.72 = 879.2

879.2 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 43.96 cm.

7 \times 2 \times 3.14 = 43.96

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

879.2 \div 43.96 = 20

The cylinder is 20 cm tall.

Answer: 20 cm

4 · Reviewdoes it hold up?

Building it back up: 307.72 for the two bases plus 43.96 times 20 for the side comes to 1186.92 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 7 medium

The cylinder at the right has a surface area of $1306.24\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 8 cm has a surface area of 1306.24 cm2. We want its height.

Givens

The base radius is 8 cm.
The surface area is 1306.24 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 8 cm, whatever the height.

8 \times 8 \times 3.14 \times 2 = 401.92

401.92 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

1306.24 - 401.92 = 904.32

904.32 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 50.24 cm.

8 \times 2 \times 3.14 = 50.24

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

904.32 \div 50.24 = 18

The cylinder is 18 cm tall.

Answer: 18 cm

4 · Reviewdoes it hold up?

Building it back up: 401.92 for the two bases plus 50.24 times 18 for the side comes to 1306.24 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 8 medium

The cylinder at the right has a surface area of $1570\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 10 cm has a surface area of 1570 cm2. We want its height.

Givens

The base radius is 10 cm.
The surface area is 1570 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 10 cm, whatever the height.

10 \times 10 \times 3.14 \times 2 = 628

628 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

1570 - 628 = 942

942 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 62.8 cm.

10 \times 2 \times 3.14 = 62.8

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

942 \div 62.8 = 15

The cylinder is 15 cm tall.

Answer: 15 cm

4 · Reviewdoes it hold up?

Building it back up: 628 for the two bases plus 62.8 times 15 for the side comes to 1570 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 9 hard

The cylinder at the right has a surface area of $2788.32\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 12 cm has a surface area of 2788.32 cm2. We want its height.

Givens

The base radius is 12 cm.
The surface area is 2788.32 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 12 cm, whatever the height.

12 \times 12 \times 3.14 \times 2 = 904.32

904.32 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

2788.32 - 904.32 = 1884

1884 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 75.36 cm.

12 \times 2 \times 3.14 = 75.36

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

1884 \div 75.36 = 25

The cylinder is 25 cm tall.

Answer: 25 cm

4 · Reviewdoes it hold up?

Building it back up: 904.32 for the two bases plus 75.36 times 25 for the side comes to 2788.32 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 10 hard

The cylinder at the right has a surface area of $4239\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 15 cm has a surface area of 4239 cm2. We want its height.

Givens

The base radius is 15 cm.
The surface area is 4239 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 15 cm, whatever the height.

15 \times 15 \times 3.14 \times 2 = 1413

1413 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

4239 - 1413 = 2826

2826 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 94.2 cm.

15 \times 2 \times 3.14 = 94.2

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

2826 \div 94.2 = 30

The cylinder is 30 cm tall.

Answer: 30 cm

4 · Reviewdoes it hold up?

Building it back up: 1413 for the two bases plus 94.2 times 30 for the side comes to 4239 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 11 hard

The cylinder at the right has a surface area of $7536\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 20 cm has a surface area of 7536 cm2. We want its height.

Givens

The base radius is 20 cm.
The surface area is 7536 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 20 cm, whatever the height.

20 \times 20 \times 3.14 \times 2 = 2512

2512 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

7536 - 2512 = 5024

5024 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 125.6 cm.

20 \times 2 \times 3.14 = 125.6

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

5024 \div 125.6 = 40

The cylinder is 40 cm tall.

Answer: 40 cm

4 · Reviewdoes it hold up?

Building it back up: 2512 for the two bases plus 125.6 times 40 for the side comes to 7536 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Variant 12 hard

The cylinder at the right has a surface area of $11775\ \text{cm}^2$ . How tall is it, in $\text{cm}$ ?

Your answer

Show solution

1 · Understandwhat's really being asked

A cylinder with base radius 25 cm has a surface area of 11775 cm2. We want its height.

Givens

The base radius is 25 cm.
The surface area is 11775 cm2.

Unknowns

The cylinder's height.

Constraints

The surface is two bases plus the curved side.

2 · Planchoose the strategy

#16 Count the Complement · also uses: #11 Work Backwards#13 Convert to Algebra

Part of the surface has nothing to do with the height: the two bases depend on the radius alone. Take them off, and what is left is a rectangle whose width is already known.

3 · Execute4 carry out the plan

1Take the two bases off

#16 Count the Complement 7.G.B.4

Each is a circle of radius 25 cm, whatever the height.

25 \times 25 \times 3.14 \times 2 = 3925

3925 cm2 that the height cannot change.

2See what is left

#11 Work Backwards 7.G.B.6

Everything else is the curved side.

11775 - 3925 = 7850

7850 cm2 of curved surface.

3Unroll the side

#13 Convert to Algebra 7.G.B.4

It is a rectangle as wide as the base is round, 157 cm.

25 \times 2 \times 3.14 = 157

Width known, height wanted.

4Divide for the height

#13 Convert to Algebra 6.EE.B.7

Area over width.

7850 \div 157 = 50

The cylinder is 50 cm tall.

Answer: 50 cm

4 · Reviewdoes it hold up?

Building it back up: 3925 for the two bases plus 157 times 50 for the side comes to 11775 cm2, the figure we were given.

Another way: Writing the whole surface as one equation in the height and solving is the same work; taking the bases off first is what stops the height appearing in two places.

Standardsmin grade 7

7.G.B.6 Solve real-world problems involving area, surface area, and volume — Splitting the cylinder's surface into bases and side.
7.G.B.4 Know the formulas for area and circumference of a circle — Finding the base's area and circumference.
6.EE.B.7 Solve one-step equations x+p=q and px=q — Solving for the height from the side's area.

💡Takeaway. Find the part of a formula the unknown does not touch and take it away first. What is left is usually one step.

Split the surface into the part the unknown touches and the part it does not · 12 practice problems

Generated variants — 12

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Givens

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