Five-Minute Check (over Lesson 12–6)

Then/Now

New Vocabulary

Key Concept: Lateral and Surface Area of Pyramids

Example 1: Surface Area of a Pyramid

Example 2: Real-World Example: Lateral Area of a Pyramid

Key Concept: Lateral and Surface Area of Cones

Example 3: Surface Area of a Cone

Over Lesson 12–6

A. 26,384.5 mm2

B. 28,274.3 mm2

C. 40,997.8 mm2

D. 41,002.3 mm2

Find the lateral area of the figure.

Over Lesson 12–6

A. 4.7 yd2

B. 4.9 yd2

C. 5.1 yd2

D. 5.3 yd2

Find the surface area of the figure.

Over Lesson 12–6

A. 1082.5 cm2

B. 1093.3 cm2

C. 1111.3 cm2

D. 1319.5 cm2

Find the surface area of a cylinder with a diameter of 12 cm and a height of 29 cm.

Over Lesson 12–6

A. 29.4 m

B. 30.7 m

C. 31.6 m

D. 32.3 m

A cylinder silo has a lateral area of 924.5 m2. The silo has a diameter of 10 meters. What is the height?

Over Lesson 12–6

A. 6,170 in2

B. 4,361 in2

C. 1,809 in2

D. 1,357 in2

Edwin has two cylindrical ottomans. He wants to place slipcovers over them so that fabric would cover the top and sides, but not the bottom. How much fabric is needed to cover both ottomans?

You have already found the surface areas of prisms and cylinders. (Lessons 12–5 and 12–6)

• Find lateral areas and surface areas of pyramids.

• Find lateral areas and surface areas of cones.

• regular pyramid

• slant height

Replace P with 8 • 4 and ℓ with 8.9

Surface Area of a Pyramid

Find the lateral and total surface area of the square pyramid.

First find the lateral area. The lateral area of the pyramid is made up of four triangles.

Write the formula.

Simplify.

Surface Area of a Pyramid

Then find the surface area. The base of the pyramid is a square.

S = L + BWrite the formula.

= L + s 2

The area of a square is s

2.

= 142.4 + 82

Substitution

= 206.4 ft 2

Simplify.

Answer: The lateral area of the square pyramid is 142.4 square feet. The surface area of the square pyramid is 206.4 square feet.

A. 16.5 m2

B. 33 m2

C. 42 m2

D. 75 m2

Find the surface area of the square pyramid.

Lateral Area of a Pyramid

CANOPIES A canopy is in the shape of a square pyramid. If the length of each side is 3.4 meters and the slant height is 2 meters, how much canvas is needed for the canopy?

Find the lateral area only, since there is no bottom to the canopy.

Write the formula for lateral area.

Replace P with 3.4 ● 4 and ℓ with 2.

Lateral Area of a Pyramid

L = 13.6 m2

Simplify.

Answer: So, 13.6 square meters of canvas was used to cover the canopy.

A. 320 ft2

B. 224 ft2

C. 160 ft2

D. 80 ft2

TENT A tent is in the shape of a square pyramid that is 8 feet on each side. The slant height is 10 feet.Find the lateral area of the tent.

Surface Area of a Cone

Find the lateral and surface areas of the cone. Round to the nearest tenth.

L = πrℓ Lateral area of a cone

= π(3.5)(10) Replace r with 3.5 and

ℓ with 10.

≈ 110.0 ft2 Simplify.

Find the lateral area.

Surface Area of a Cone

Find the surface area.

S = L + πr 2

Surface area of a cone

≈ 110 + π(3.5)2

Replace L with 110 and r with 3.5.

≈ 148.5 ft2 Simplify.

Answer: The lateral area is about 110.0 square feet and the surface area is about 148.5 square feet.

A. 376.1 cm2

B. 587.4 cm2

C. 963.5 cm2

D. 1028.0 cm2

Find the surface area of the cone. Round to the nearest tenth.