Question

An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet tall and has a base with a circumference of 22.608 ​feet, what is the volume of the​ sculpture? Use 3.14 for pi.

Answer 1

The volume of the sculpture is 67.824 ft^3

Explanation:

In this question, we are to calculate the volume of a conical sculpture, given the height of the sculpture and the circumference of the base.

Mathematically, the volume V of the sculpture is given by;

V =1/3 * π * r^2 * h

Now, we have the height directly from the question but we do not have the value of the radius.

We can obtain the value of the radius from the circumference of the base

Mathematically, the circumference C of the base of the cone is given by;

C = 2 * π * r

Inputing the value of the circumference, we have;

22.608 = 2 * 3.14 * r

r = 22.608/(2 * 3.14)

r = 22.608/6.28

r = 3.6 feet

Now plugging these values into the volume equation, we have

V = 1/3 * 3.14 * 3.6^2 * 5

V = 67.824 ft^3