Five-Minute Check (over Lesson 12–5)

Then/Now

Key Concept: Lateral and Surface Area of Cylinders

Example 1: Surface Area of a Cylinder

Example 2: Real-World Example: Compare Surface Areas of Cylinders

Over Lesson 12–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 197.6 cm2

B. 204.7 cm2

C. 247.6 cm2

D. 274.4 cm2

Find the lateral area of the figure.

Over Lesson 12–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 96 in2

B. 98 in2

C. 106 in2

D. 108 in2

Find the surface area of the figure.

Over Lesson 12–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 2.4 m2

B. 2.6 m2

C. 3.6 m2

D. 3.8 m2

Find the lateral area of a cube with a length of 0.8 meter.

Over Lesson 12–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 512 in2

B. 520 in2

C. 570 in2

D. 594 in2

Amy needs to wrap a box that is 18 inches long, 11 inches wide, and 3 inches high. What is the minimum amount of wrapping paper that she needs?

Over Lesson 12–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3,360 in2

B. 5,760 in2

C. 7,630 in2

D. 28,800 in2

How much wood is needed to make a rectangular toy box that measures 40 inches long, 30 inches wide, and 24 inches high?

You have already found the lateral areas and surface areas of prisms. (Lesson 12–5)

• Find lateral and surface areas of cylinders.

• Compare surface areas of cylinders.

Surface Area of a Cylinder

A. Find the lateral area and surface area of the cylinder. Round to the nearest tenth.

Lateral Area

L = 2πrh

= 2π(5)(8)

= 80πexact answer

≈ 251.3 in2

approximate answerThe lateral area is about 251.3 square inches.

Surface Area of a Cylinder

Surface Area

S = L + 2πr2

= 80π + 2π(5)2

= 130π exact answer

≈ 408.4 in2

approximate answer

The surface area is about 408.4 square inches.

Answer: L ≈ 251.3 in2, S ≈ 408.4 in2

Surface Area of a Cylinder

The lateral area is about 537.2 square feet.

Lateral Area

L = 2πrh

= 2 • π • 9 • 9.5

= 171π

= 537.2 ft2

B. Find the lateral area and surface area of the cylinder.

diameter of 18 feet and height of 9.5 feet

The diameter is 18 feet, so the radius is or 9 feet.

Surface Area

S = L + 2πr2

= 171π + 2π(9)2

= 171π + 162π

≈ 1046.2 ft2

Surface Area of a Cylinder

The surface area is about 1046.2 square feet.

Answer: L ≈ 537.2 ft2, S ≈ 1046.2 ft2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. lateral area, 1082.0 in2; surface area, 1504.4 in2

B. lateral area, 1082.0 in2; surface area, 3852.9 in2

C. lateral area, 2163.9 in2; surface area, 2586.4 in2

D. lateral area, 4436.1 in2; surface area, 4858.6 in2

A. Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. lateral area, 47.1ft2; surface area, 56.5 ft2

B. lateral area, 94.2 ft2; surface area, 150.8 ft2

C. lateral area, 141.4 ft2; surface area, 197.9 ft2

D. lateral area, 188.5 ft2; surface area, 301.6 ft2

B. Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. diameter of 6 feet and height of 5 feet

Compare Surface Areas of Cylinders

MANUFACTURING A company manufactures dowel rods. Rod A has a diameter of 3 inches and a height of 12 inches. Rod B has a diameter of 1 inch and a height of 36 inches. Which rod has the larger surface area?

The diameter of Rod A is 3 inches, so radius is 1.5 inches. Its height is 12 inches.

The diameter of Rod B is 1 inch, so radius is 0.5 inch. Its height is 36 inches.

Find the surface area of both rods.

Compare Surface Areas of Cylinders

Rod A

S = L + 2πr 2

= 2πrh + 2πr 2

= 2π(1.5)(12) + π(1.5)2

= 36π + 2.25π

≈ 120.2 in2

Rod B

S = L + 2πr 2

= 2πrh + 2πr 2

= 2π(0.5)(36) + π(0.5)2

= 36π + 0.25π

≈ 113.9 in2

Answer: Rod A has the larger surface area.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. Brand A’s container has the larger surface area.

B. Brand B’s container has the larger surface area.

C. The containers have the same surface area.

D. It is not possible to determine the surface areas of the containers.

A cylindrical Brand A oatmeal container has a radius of 5 inches and a height of 12 inches. Brand B uses a cylinder with a radius of 4 inches and a height of 14 inches. Which statement is true?