The sphere and the ball

Sphere or ball?

A sphere is the surface (like the skin of a ball), whilst a ball is the solid object (the whole ball, including its interior). In practice, the volume formula applies to the ball.

Volume formula

For a sphere of radius r:

V = (4/3) × π × r³

Example: a sphere with radius r = 3 cm: V = (4/3) × π × 3³ = (4/3) × π × 27 = 36 × π ≈ 113.1 cm³

Example using a diameter

If a diameter d = 10 cm is given, we must first find the radius: r = d / 2 = 5 cm, then apply the formula: V = (4/3) × π × 5³ = (4/3) × π × 125 ≈ 523.6 cm³

Summary table of formulas

Solid	Volume formula
Cube (edge length c)	V = c³
Rectangular prism (L, l, h)	V = L × l × h
Cylinder (r, h)	V = π × r² × h
Pyramid (base, h)	V = (Base area × h) / 3
Cone (r, h)	V = (π × r² × h) / 3
Sphere (r)	V = (4/3) × π × r³

Common pitfall to avoid

Don’t forget to raise r to the third power (r³) in the formula for the sphere, rather than to the second power as with the cylinder or the cone. This is the most common mistake made with this solid.