Question

An artist makes a cone-shaped sculpture for an art exhibit. If the sculpture is 7 feet tall and has a base with a circumference of 24.492 feet, what is the volume of the sculpture? Use 3.14 for p, and round to the nearest hundredth.

Answer 1

Answer:

The volume of the sculpture is 111.439 $feet^{3}$  

Step-by-step explanation:

In this question, we are concerned with calculating the of the sculpture made given the information in the question.

To get the volume, we use the formula for the volume of a cone.

Mathematically, V = 1/3 × π × $r^{2}$ × h

From the question, we have the height but we do not know what the radius is. The information concerning the radius given in the question is that the circumference of the base of the cone is 24.492 feet

Mathematically, the formula for the circumference of a circle is

C = 2×π×r

From the question, we can identify that the circumference is 24.492 feet and we are expected to use the value of 3.14 for π

We plug these values into the equation for the circumference

24.492 = 2 ×3.14 × r

r = $\frac{24.492}{2 * 3.14}$

r = 24.492/6.28

r = 3.9 feet

We now plug this value of the radius alongside the value for the height into the equation for the volume given above

V = 1/3 × 3.14 × $3.9^{2}$ × 7

V = 111.4386 = 111.439 $feet^{3}$ to the nearest hundredth