Volume of cone radius 5 height 6

Step by step

The question

Question: find the volume of a cone with radius 5 and height 6.

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 = 5 and h = 6.

5² means 5 times 5.

That is 25.

So V = ⅓ × π × 25 × 6.

Keep the numbers small: divide 6 by 3 first.

6 divided by 3 is 2.

So V = π × 25 × 2.

25 times 2 is 50.

So V = 50π.

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.

50 times 3.14 is 157.

So the volume is about 157 cubic units.

Let's look back.

First: a third of the cylinder.

Last: about how much.