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.
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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?