Volume of pyramid square base 3 height 5

Step by step

The question

Question: find the volume of a pyramid with a square base 3 by 3 and height 5.

1 Area of the base

The base is a square, 3 by 3.

Its area is side times side: A = 3 × 3.

3 times 3 is 9.

So the base is A = 9 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 = 9 and height = 5.

Keep the numbers small: divide 9 by 3 first.

9 divided by 3 is 3.

So V = 3 × 5.

3 times 5 is 15.

So the volume is 15 cubic units.

Let's look back.

First: area of the base.

Last: a third of the box.