Volume of a Sphere Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

A sphere has a diameter of 10 cm. Find its volume. Leave your answer in terms of

\pi

1
Step 1: The radius is half the diameter: $r = 10/2 = 5$ cm.
2
Step 2: $V = \frac{4}{3}\pi (5)^3 = \frac{4}{3}\pi \times 125 = \frac{500\pi}{3}$ cm³.

Answer

V = \dfrac{500\pi}{3}

cm³.

Always convert diameter to radius before substituting into the sphere formula. With

r = 5

, we get

r^3 = 125

, and

\frac{4}{3} \times 125 = \frac{500}{3}

, giving

V = \frac{500\pi}{3}

About Volume of a Sphere

The amount of three-dimensional space inside a sphere, given by $\frac{4}{3}\pi r^3$ .

A basketball has a radius of 12 cm. Find its volume. Leave your answer in terms of [formula].

A sphere has a volume of [formula] cm³. Find its radius.

If the radius of a sphere is doubled, by what factor does its volume increase? Prove your answer alg