1. Find the surface area of a cylinder with r = 10 and h = 6. Round to the nearest tenth.

2. Find the surface area of a cylinder with r = 4.5 and

h = 6.3. Round to the nearest tenth.

3. Find the surface area of the cylinder

shown to the nearest tenth.

4. What is the height of a cylinder with

radius of 4 centimeters and surface

area of 80 square centimeters?

• regular pyramid

• slant height

• Find lateral areas of regular pyramids.

• Find surface areas of regular pyramids.

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CANDLES A candle store offers a pyramidal candle that burns for 20 hours. The square base is 6 centimeters on a side and the slant height of the candle is 22 centimeters. Find the lateral area of the candle.

Find Lateral Area

We need to find the lateral area of the square pyramid. The sides of the base measure 6 centimeters, so the perimeter is

Answer: The lateral area of the candle is 264 square centimeters.

Find Lateral Area

Lateral area of a regular pyramid

Multiply.

A. A

B. B

C. C

D. D

A. 25.9 ft2

B. 51.8 ft2

C. 103.6 ft2

D. 207.2 ft2

CAMPING A tent in the shape of a pyramid is put up by two campers. The square base is 7 feet on a side and the slant height of the tent is 7.4 feet. Find the lateral area of the tent.

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Surface Area of a Square Pyramid

Find the surface area of the square pyramid. Round to the nearest tenth if necessary.

To find the surface area, first find the slant height of the pyramid. The slant height is the hypotenuse of a right triangle with legs that are the altitude and a segment with a length that is one-half the side measure of the base.

Surface Area of a Square Pyramid

Pythagorean Theorem

Simplify.

Now find the surface area of a square pyramid. The perimeter of the base is and the area of the base is

Surface Area of a Square Pyramid

Answer: The surface area is 179.4 square meters to the nearest tenth.

Use a calculator.

Surface area of a square pyramid

1. A

2. B

3. C

4. D

A. 73.8 m2

B. 89.8 m2

C. 163.5 m2

D. 696 m2

Find the surface area of the square pyramid to the nearest tenth.

Surface Area of a Regular Pyramid

Find the surface area of the regular pyramid. Round to the nearest tenth.

The altitude, slant height, and apothem form a right triangle. Use the Pythagorean Theorem to find the apothem. Let x represent the length of the apothem.

Surface Area of a Regular Pyramid

Pythagorean Theorem

Simplify.

Now find the length of the sides of the base. The central

angle of the hexagon measures Let a

represent the measure of the angle formed by a radius

and the apothem.

Surface Area of a Regular Pyramid

Use trigonometry to find the length of the sides.

Multiply each side by 2.

Multiply each side by 9.

Use a calculator.

Surface Area of a Regular Pyramid

Next, find the perimeter and area of the base.

Surface Area of a Regular Pyramid

Finally, find the surface area.

Answer: The surface area is approximately 748.2 square centimeters.

Surface area of a regular pyramid

Simplify.

1. A

2. B

3. C

4. D

A. 236.1 cm2

B. 326.9 cm2

C. 90.8 cm2

D. 417.7 cm2

Find the surface area of the regular pentagonal pyramid.