Volume of a sphere, step by step
The volume of a sphere is four-thirds π r cubed.
The question
Volume of a sphere, diameter 12 cm
diameter: 12 cm
12 ÷ 2=6
6 × 6 × 6=216
4/3 × 3.14 ×216=904.32
904.32 cm³
- The 12 cm marked here goes right ACROSS the sphere — that is the diameter. The formula wants the radius, and using the diameter instead makes the answer EIGHT times too big, because it is cubed.
- Half of 12 is 6, so r = 6 cm.
- Cube the radius on a line of its own. r³ means r × r × r, not r × 3: 6 × 6 × 6 = 216.
- Then four-thirds of that, times π: 4/3 × 3.14 × 216 = 904.32.
- So the volume is 904.32 cubic cm. Cubic, not square — a volume fills a space, and the unit is the quickest way to notice you have answered a surface-area question instead.
How it works.
- 01
The 12 cm marked here goes right ACROSS the sphere — that is the diameter. The formula wants the radius, and using the diameter instead makes the answer EIGHT times too big, because it is cubed.
- 02
Half of 12 is 6, so r = 6 cm.
- 03
Cube the radius on a line of its own. r³ means r × r × r, not r × 3: 6 × 6 × 6 = 216.
- 04
Then four-thirds of that, times π: 4/3 × 3.14 × 216 = 904.32.
- 05
So the volume is 904.32 cubic cm. Cubic, not square — a volume fills a space, and the unit is the quickest way to notice you have answered a surface-area question instead.