Sphere volume without the fear of π

Remember V = 4/3 πr³, keep radius not diameter, and leave π exact unless asked otherwise.

Key formulas

If the question gives a diameter of 10 cm, the radius is 5 cm. Substituting the diameter by mistake multiplies the volume by eight.

r = 3 cm → V = (4/3)π(27) = 36π cm³. Leave the answer as 36π unless a decimal is required.

A sphere of radius 3 sits inside a 6×6×6 cube. The cube has volume 216. 36π ≈ 113, which is less than 216, so the size is believable.

Problem. Find the volume of a sphere of diameter 12 cm, in terms of π.

Solution. Radius r = 6. V = (4/3)πr³ = (4/3)π × 216 = 288π cm³.

Diameter 6 → r = 3 → V = 36π, not (4/3)π(216).

Sphere radius 3 cm. Volume is:

That is surface area, not volume.