An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet tall and has total volume 109.9 cubic​ feet, what is the radius of the​ sculpture? Use 3.14 for pie

Verified Answer :

Cone Volume = (π • r² • h) ÷ 3
109.9 = PI 5 radius^2 / 3
3 109.9 / (3.14 5) = radius^2



329.7



/ 15.7

radius^2 = 21

radius = 4.582575695






The radius of cone-shaped sculpture is 4.582575695.

What is cone?

A cone is "three dimensional shape that narrows smoothly from a flat base to a point".

According to the question,

The sculpture is in cone shape which has 5 feet tall and has total volume of cone 109.9 cubic feet.

Formula for volume of cone = \(\frac{1}{3}\) π.r².h

109.9 = \(\frac{1}{3}\) ×\(\frac{22}{7}\) × r² ×5

109.9 = (110/21) .r²

109.9 × \(\frac{21}{110}\) = r²

\(\frac{2307.9}{110}\) = r²

20.981 = r²

r =4.582575695... ≈ 4.59.

Hence, the radius of cone-shaped sculpture is 4.582575695.

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