Volume of cone radius 2 height 5

Step by step

The question

Question: find the volume of a cone with radius 2 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 = 2 and h = 5.

2² means 2 times 2.

That is 4.

So V = ⅓ × π × 4 × 5.

None of the numbers divides by 3.

So we multiply and keep the 3 at the bottom: 4 times 5 is 20.

So V = 20π over 3.

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.

20 times 3.14 is 62.8.

62.8 divided by 3 is about 20.93.

So the volume is about 20.93 cubic units.

Let's look back.

First: a third of the cylinder.

Last: about how much.