Volume of pyramid square base 6 height 4

Step by step

The question

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

1 Area of the base

The base is a square, 6 by 6.

Its area is side times side: A = 6 × 6.

6 times 6 is 36.

So the base is A = 36 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 = 36 and height = 4.

Keep the numbers small: divide 36 by 3 first.

36 divided by 3 is 12.

So V = 12 × 4.

12 times 4 is 48.

So the volume is 48 cubic units.

Let's look back.

First: area of the base.

Last: a third of the box.