Step by step
The question
Question: find the volume of a sphere (a ball) with radius 2.
1 Use the rule
Put the ball in a cylinder just as wide and just as high.
The ball fills exactly two thirds of that cylinder.
Worked out, that gives the rule for a ball.
The rule has r³: r times r times r.
Careful: it is not 3 times r.
π is a special number for circles.
It is about 3.14.
So the volume is V = 4/3 × π × r³.
Now put the numbers in: r = 2.
2³ means 2 times 2 times 2.
That is 8.
So V = 4/3 × π × 8.
None of the numbers divides by 3.
So we multiply and keep the 3 at the bottom: 4 times 8 is 32.
So V = 32π over 3.
We keep π in the answer.
That is the exact answer.
2 About how much
To see about how much, put 3.14 for π.
32 times 3.14 is 100.48.
100.48 divided by 3 is about 33.49.
So the volume is about 33.49 cubic units.
Let's look back.
First: use the rule.
Last: about how much.