Question

An artist creates a cone-shaped sculpture for an art exhibit. If the sculptor is 5 feet tall and has a base with a circumference of 20.096 feet, what is the volume of the sculpture? Use 3.14 for pie

Answer 1

V = 53.5893 ft^3 .... (= 53.6 ft^3)

Explanation:

Given:-

- The height of cone, h = 5 ft

- The circumference of base, c = 20.096 ft

Find:-

What is the volume of the cone-shaped sculpture?

Solution:-

- The volume of a cone (V) is given by:

V = pi/3*r^2*h

Where, r = radius of circular base

- To determine (r) we will use the formula for the circular base:

c = 2*pi*r

r = 20.096 / 2*3.14

r = 3.2 ft

- Now evaluate the volume V:

V = 3.14/3 * (3.2)^2 * 5

V = 53.5893 ft^3 .... (= 53.6 ft^3)

Answer 2

The volume of the sculpture is 53.589 ft³

Explanation:

Here, we note that the volume of a right circular cone is given by

`V = \pi r^2(h)/(3)`

Where:

V = Volume of the right circular cone

r = Radius of the base of the cone

h = Height of the cone = 5 ft

π = Constant = 3.14

However, the circumference is given as

Circumference = 20.096 ft

The formula for circumference is

Circumference = 2πr

Therefore, 2πr = 20.096 ft and

`r = (20.096 ft)/(2* \pi ) = (20.096 ft)/(2* 3.14)=3.2\, ft`

Therefore,

`V = \pi r^2(h)/(3) = 3.14 * 3.2^2 *(5)/(3) = 53.589 \, ft^3`.