Applications with Volume of Cones

The volume of a cone is 88π cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown. What is Fatima's error?

• In step 4, Fatima did not find the correct value of 8/3(88).

• In step 2, Fatima should not have multiplied (1/3) and 8.

• In step 3, Fatima did not multiply 88 by the reciprocal of (8/3).

• In step 1, Fatima did not substitute the correct value for the height in the formula.

An icicle is in the shape of an inverted cone with a diameter of 9 mm and a height of 120 mm. The icicle drips at a rate of 75 mm³ per minute. How long will it take the icicle to completely melt? Use 3.14 for π. Round the answer to the nearest tenth.

• 5.1 minutes

• 7.5 minutes

• 15.1 minutes

• 33.9 minutes

Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Fill in the blank to make the statement true. Use 3.14 for π. Round to the nearest hundredth.

The volume of the green candle is about _______ in³.

Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Fill in the blank to make the statement true. Use 3.14 for π.

The diameter of the green candle is _____ inches.

Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Fill in the blank to make the statement true. Use 3.14 for π. Round to the nearest hundredth.

The base area of the green candle is about _____ in².

Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Fill in the blank to make the statement true. Use 3.14 for π.

The price of one green candle is about $______.

A circular cardboard piece is needed for the base of a volcano model. The volcano is 46 centimeters tall and has a volume of 800 cubic centimeters. Which equation can be used to find the area of the circular base?

• 46 = (1/3)(B)²(800)

• 46 = (1/3)(B)(800)

• 800 = (1/3)(B)²(46)

• 800 = (1/3)(B)(46)

What is the height of the cone?

• 5 cm

• 6 cm

• 15 cm

• 30 cm

What is the height of the cone?

• 3 in.

• 9 in.

• 27 in.

• 75 in.

The volume of a cone with a radius of 7 cm is 147π cubic centimeters. Which expression can be used to find h, the height of the cone?

• 147π = (1/3)(7)(h)²

• 147π = (1/3)π(7²)(h)

• 147π = (1/3)π(h)

• 147π = (1/3)π(7)(h)