Step by step
The question
Question: find the surface area of a sphere (a ball) with radius 5 cm.
1 Use the rule
Cut the ball in half.
The flat circle inside has area π × r².
The skin of the ball covers exactly 4 of these circles.
Like the peel of an orange.
Archimedes found this, long ago.
π is a special number for circles: the way round is about 3.14 times the way across.
So the surface area is S = 4 × π × r².
S = 4 × π × r2
Now put the numbers in: r = 5.
S = 4 × π × 52
5² means 5 times 5.
That is 25.
52 = 5 × 5
= 25
So S = 4 × π × 25.
S = 4 × π × 25
4 times 25 is 100.
So S = 100π.
We keep π in the answer.
That is the exact answer.
S = 100π cm2
2 About how much
To see about how much, put 3.14 for π.
S ≈ 100 × 3.14
100 times 3.14 is 314.
So the surface area is about 314 cm².
S ≈ 314 cm2
Let's look back.
First: use the rule.
Last: about how much.
Answer
S ≈ 314 cm2