Step by step
The question
Question: find the volume of a cone with diameter 6 and height 4.
1 Find the radius
The diameter goes all the way across the circle.
The radius is half of it.
Half of 6 is 6 divided by 2.
6 divided by 2 is 3.
So r = 3.
2 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.
It is about 3.14.
The cylinder is π × r² × h.
So the cone is V = ⅓ × π × r² × h.
Now put the numbers in: r = 3 and h = 4.
3² means 3 times 3.
That is 9.
So V = ⅓ × π × 9 × 4.
Keep the numbers small: divide 9 by 3 first.
9 divided by 3 is 3.
So V = π × 3 × 4.
3 times 4 is 12.
So V = 12π.
We keep π in the answer.
That is the exact answer.
3 About how much
To see about how much, put 3.14 for π.
12 times 3.14 is 37.68.
So the volume is about 37.68 cubic units.
Let's look back.
First: find the radius.
Then: a third of the cylinder.
Last: about how much.