Volume of pyramid square base 5 height 4

Step by step

The question

Question: find the volume of a pyramid with a square base 5 by 5 and height 4.

1 Area of the base

The base is a square, 5 by 5.

Its area is side times side: A = 5 × 5.

5 times 5 is 25.

So the base is A = 25 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 = 25 and height = 4.

None of the numbers divides by 3.

So we multiply and keep the 3 at the bottom: 25 times 4 is 100.

So the volume is 100/3 cubic units.

100 divided by 3 is about 33.33.

So the volume is about 33.33 cubic units.

Let's look back.

First: area of the base.

Last: a third of the box.