Volume of pyramid square base 12 cm height 10 cm

Step by step

The question

Question: find the volume of a pyramid with a square base 12 cm by 12 cm and height 10 cm.

1 Area of the base

The base is a square, 12 by 12.

Its area is side times side: A = 12 × 12.

12 times 12 is 144.

So the base is A = 144 cm².

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 = 144 and height = 10.

Keep the numbers small: divide 144 by 3 first.

144 divided by 3 is 48.

So V = 48 × 10.

48 times 10 is 480.

So the volume is 480 cm³.

Let's look back.

First: area of the base.

Last: a third of the box.