Surface area of a sphere, step by step
The surface area of a sphere is 4πr², and at π = 3.14 that is 12.56 times the radius squared.
Surface area of a sphere, diameter 12 cm
- 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 FOUR times too big, because it is squared.
- Half of 12 is 6, so r = 6 cm.
- Square the radius on a line of its own. r² means r × r, not r × 2: 6 × 6 = 36.
- Now four times π, times that: 4 × 3.14 is 12.56, and 12.56 × 36 = 452.16. Nothing to round — 12.56 times a whole number always lands on a whole number of hundredths.
- So the surface area is 452.16 square cm. Square, not cubic — a surface is skin rather than space, and the unit is the quickest way to notice you have answered the volume 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 FOUR times too big, because it is squared.
- 02
Half of 12 is 6, so r = 6 cm.
- 03
Square the radius on a line of its own. r² means r × r, not r × 2: 6 × 6 = 36.
- 04
Now four times π, times that: 4 × 3.14 is 12.56, and 12.56 × 36 = 452.16. Nothing to round — 12.56 times a whole number always lands on a whole number of hundredths.
- 05
So the surface area is 452.16 square cm. Square, not cubic — a surface is skin rather than space, and the unit is the quickest way to notice you have answered the volume question instead.