Question

There is a sphere with a diameter 6x cm, which of the following expressions best represents the volume of this sphere in cubic centimeters in terms of pi?

A. 4/3 pi (3x)^3
B. 4/3 pi (6x)^3
C. 4 pi (3x)^2
D. 4 pi (6x)^2

Answer 1

A. 4/3 pi (3x)^3.

Explanation:

Volume of a sphere = (4/3) π r^3.

The diameter = 6x so the radius = 3x.

Thus the volume of our sphere =

(4/3) π (3x)^3 (answer).

Answer 2

The volume (V) of a sphere can be calculated using the formula V = 4/3 * pi * r^3, where r is the radius of the sphere.

For a sphere with a diameter of 6x cm, the radius would be 1/2 the diameter. So, the radius (r) of this sphere is (6x)/2 = 3x cm.

Substituting this value for r in the original volume formula we get:
V = 4/3 * pi * (3x)^3

That is the expression represents the volume of the sphere with diameter 6x cm in terms of pi and x. So, the correct choice letter is A.

Answer:A. 4/3 pi (3x)^3