Volume of pyramid square base 9 m height 2 m

Step by step

The question

Question: find the volume of a pyramid with a square base 9 m by 9 m and height 2 m.

1 Area of the base

The base is a square, 9 by 9.

Its area is side times side: A = 9 × 9.

9 times 9 is 81.

So the base is A = 81 m².

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 = 81 and height = 2.

Keep the numbers small: divide 81 by 3 first.

81 divided by 3 is 27.

So V = 27 × 2.

27 times 2 is 54.

So the volume is 54 m³.

Let's look back.

First: area of the base.

Last: a third of the box.