Step by step
The question
Question: find the volume of a sphere (a ball) with radius 3.
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 = 3.
3³ means 3 times 3 times 3.
That is 27.
So V = 4/3 × π × 27.
Keep the numbers small: divide 27 by 3 first.
27 divided by 3 is 9.
So V = 4 × π × 9.
4 times 9 is 36.
So V = 36π.
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.
36 times 3.14 is 113.04.
So the volume is about 113.04 cubic units.
Let's look back.
First: use the rule.
Last: about how much.