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Surface area of sphere radius 2 cm

Step by step, with the reason for every step · Spheres and hemispheres · Geometry

Step by step

The question

Question: find the surface area of a sphere (a ball) with radius 2 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.

π is a special number for circles.

It is about 3.14.

So the surface area is S = 4 × π × r².

S = 4 × π × r2

Now put the numbers in: r = 2.

S = 4 × π × 22

2² means 2 times 2.

That is 4.

22 = 2 × 2 = 4

So S = 4 × π × 4.

S = 4 × π × 4

4 times 4 is 16.

So S = 16π.

We keep π in the answer.

That is the exact answer.

S = 16π cm2

2 About how much

To see about how much, put 3.14 for π.

S ≈ 16 × 3.14

16 times 3.14 is 50.24.

So the surface area is about 50.24 cm².

S ≈ 50.24 cm2

Let's look back.

First: use the rule.

Last: about how much.

Answer
S ≈ 50.24 cm2

Your turn

Try this one yourself, then check:

Find the surface area.
Show the answer
S ≈ 12.56 cm2

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