Question

The volume of a sphere is V = 4/3 pi r³

and the relationship between d the radius r and the diameter d is r = d/2.

Find the volume of the sphere in terms of the diameter d and simplify the expressions.
What is the volume of the sphere when the diameter is 2/3 centimeter?​

Answer 1

Substituting the relationship between the radius and diameter in the formula for the volume of a sphere, we have:

V = (4/3) x π x (d/2)^3

Simplifying the expression inside the parentheses:

(d/2)^3 = d^3/8

Substituting again:

V = (4/3) x π x (d^3/8)

Simplifying:

V = π x d^3/6

When the diameter is 2/3 centimeter, we have:

V = π x (2/3)^3/6
V = π x 8/162
V = 4π/81 cubic centimeters (in terms of π)

Or approximately:

V ≈ 0.0524 cubic centimeters (rounded to four decimal places)