Volume of cone radius 3 height 5

Step by step

The question

Question: find the volume of a cone with radius 3 and height 5.

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.

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 = 5.

3² means 3 times 3.

That is 9.

So V = ⅓ × π × 9 × 5.

Keep the numbers small: divide 9 by 3 first.

9 divided by 3 is 3.

So V = π × 3 × 5.

3 times 5 is 15.

So V = 15π.

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.

15 times 3.14 is 47.1.

So the volume is about 47.1 cubic units.

Let's look back.

First: a third of the cylinder.

Last: about how much.