Volume of cone radius 3 height 4 Step by Step

Step by step

Question: find the volume of a cone with radius 3 and height 4.

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.

V = 13 × π × r² × h

Now put the numbers in: r = 3 and h = 4.

V = 13 × π × 3² × 4

3² means 3 times 3.

That is 9.

3² = 3 × 3 = 9

So V = ⅓ × π × 9 × 4.

V = 13 × π × 9 × 4

Keep the numbers small: divide 9 by 3 first.

9 divided by 3 is 3.

93 = 3

So V = π × 3 × 4.

V = π × 3 × 4

3 times 4 is 12.

So V = 12π.

We keep π in the answer.

That is the exact answer.

V = 12π

To see about how much, put 3.14 for π.

V ≈ 12 × 3.14

12 times 3.14 is 37.68.

So the volume is about 37.68 cubic units.

V ≈ 37.68

Let's look back.

First: a third of the cylinder.

Last: about how much.

Answer

V ≈ 37.68