Jean-Paul Sovique, the famous sculptor, is building a solid conical sculpture. He has 1,178.1 cubic feet of clay to work with, and he wants his sculpture to be three times as high as its radius. What will the radius and height of his cone be?

Question

Mathematics

Sadie

4 January, 09:09

Jean-Paul Sovique, the famous sculptor, is building a solid conical sculpture. He has 1,178.1 cubic feet of clay to work with, and he wants his sculpture to be three times as high as its radius. What will the radius and height of his cone be?

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Answers (1)

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Wyatt Parrish · Answer 1

Radius = 7.21 feet.

Height = 21.63 feet

- to the nearest hundredth.

Step-by-step explanation:

Let the radius be r feet, then the height will be 3r feet.

So the volume = 1,178.1 = 1/3 π r^2 h

1.178.1 = 1/3 π r^2 3r

1/3 π 3 r^3 = 1178.1

π r^3 = 1178.1

r^3 = 1178.1 / π

r^3 = 375

r = 7.211 feet.

So the height = 3 * 7.211 ft

= 21.633 ft