Back to courseLesson 4 of 4

Spheres

What you'll learn

Meet the sphere's volume and surface area, and why cubing the radius makes it grow so fast.

The sphere is the odd one out — no flat base to stack. Its volume and its surface area each have a formula worth knowing.

Volume

V = 4⁄3 π r³

A sphere of radius 3: 4/3 × π × 27 ≈ 113.1 cubic units. The radius is cubed, so doubling it makes the sphere eight times bigger — that's why a beach ball dwarfs a baseball.

Surface area

The skin of a sphere is SA = 4 π r² — exactly four times the area of the circle you'd get by slicing through its middle. For that radius-3 sphere: 4 × π × 9 ≈ 113.1 square units. (Volume and surface area come out to the same number only at r = 3 — a coincidence, not a rule.)

Check your understanding

Question 1 of 2

You double a sphere's radius. Its volume becomes how many times bigger?