Question

A sphere has a diameter of 36 meters. What its exact volume?

Answer 1

V = 7776 pi m^3

Explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We need to know the radius

r = d/2 = 36/2 = 18

V = 4/3 pi (18)^3

V = 4/3 * pi *5832

V = 7776 pi

We cannot approximate pi since we want the exact answer

Answer 2

7776π cubic meters.

Explanation:

Recall the volume formula for a sphere is

V = (4/3) π r^3

r = (1/2)*diameter = (1/2)*36 m = 18 meters

V = (4/3)*π*(18)^3 = 24,429.02447 cubic meters

However the problem wants an exact answer, and not an approximation, therefore I will express the volume in terms of simplified expressions.

V = (4/3)*π*(18)^3 = (4/3)*π * (3*6)^3 = 4 *π * (1/3)*(3^3) *(6^3)

V = 4 *π * (1/3)*(3^3) *(6^3) = 4*π * 9 * 6^3 = 7776π cubic meters.