1. Find the surface area of the regular pyramid shown. Round to the nearest tenth if necessary.

2. Find the surface area of the regular pyramid shown. Round to the nearest tenth if necessary.

3. What is the slant height of a square pyramid with base lengths of 15 inches and height of 10 inches?

• circular cone

• right cone

• oblique cone

• Find lateral areas of cones.

• Find surface areas of cones.

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Explore We are given the altitude and the diameter of the

base. We need to find the slant height of the cone.

Lateral Area of a Cone

Plan The radius of the base, height, and slant height form a right triangle. Use the Pythagorean Theorem to solve for the slant height. Then use the formula for the lateral area of a right circular cone.

Lateral Area of a Cone

Next, use the formula for the lateral area of a right circular cone.

Lateral Area of a Cone

Solve Write an equation and solve for .

Simplify.

Pythagorean Theorem

Take the square root of each side.

Lateral area of a cone

Use a calculator.

Answer: The lateral area is approximately 31.8 square inches.

Lateral Area of a Cone

Check Use estimation to check the reasonableness of this result. The lateral area is approximately 3 ● 1.25 ● 8 or 30 square inches. Compared to the estimate, the answer is reasonable.

A. A

B. B

C. C

D. D

A. 73.4 in2

B. 70.7 in2

C. 141.4 in2

D. 146.7 in2

A hat for a child’s birthday party has a conical shape with an altitude of 9 inches and a diameter of 5 inches. Find the lateral area of the birthday hat. Round to the nearest tenth.

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Surface Area of a Cone

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

Answer: The surface area is approximately 20.2 square centimeters.

Surface area of a cone

Use a calculator.

1. A

2. B

3. C

4. D

A. 124.6 cm2

B. 80.2 cm2

C. 63.6 cm2

D. 20.2 cm2

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