Volume of pyramid square base 4 height 6

Step by step

The question

Question: find the volume of a pyramid with a square base 4 by 4 and height 6.

1 Area of the base

The base is a square, 4 by 4.

Its area is side times side: A = 4 × 4.

4 times 4 is 16.

So the base is A = 16 square units.

2 A third of the box

Draw a box around the pyramid, with the same base and the same height.

Fill the pyramid with sand 3 times.

That fills the box exactly.

So the pyramid is one third of the box.

The box is A times height.

So the pyramid is V = ⅓ × A × height.

Now put the numbers in: A = 16 and height = 6.

Keep the numbers small: divide 6 by 3 first.

6 divided by 3 is 2.

So V = 16 × 2.

16 times 2 is 32.

So the volume is 32 cubic units.

Let's look back.

First: area of the base.

Last: a third of the box.