Step by step
The question
Question: find the volume of a cone with radius 4 cm and height 9 cm.
1 A third of the cylinder
Draw a cylinder around the cone, with the same base and the same height.
Fill the cone with water 3 times.
That fills the cylinder exactly.
So the cone is one third of the cylinder.
π is a special number for circles: the way round is about 3.14 times the way across.
The cylinder is circle area times height: π × r² × h.
So the cone is V = ⅓ × π × r² × h.
Now put the numbers in: r = 4 and h = 9.
4² means 4 times 4.
That is 16.
So V = ⅓ × π × 16 × 9.
⅓ of 9 means 9 divided by 3.
We can multiply in any order.
So we do that first: it keeps the numbers small.
9 divided by 3 is 3.
So ⅓ × 9 becomes 3.
So V = π × 16 × 3.
16 times 3 is 48.
So V = 48π.
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.
48 times 3.14 is 150.72.
So the volume is about 150.72 cm³.
Let's look back.
First: a third of the cylinder.
Last: about how much.