Volume of pyramid base 10 by 6 height 9

Step by step

The question

Question: find the volume of a pyramid with a rectangle base 10 by 6 and height 9.

1 Area of the base

The base is a rectangle, 10 by 6.

Its area is length times width: A = 10 × 6.

10 times 6 is 60.

So the base is A = 60 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 = 60 and height = 9.

Keep the numbers small: divide 60 by 3 first.

60 divided by 3 is 20.

So V = 20 × 9.

20 times 9 is 180.

So the volume is 180 cubic units.

Let's look back.

First: area of the base.

Last: a third of the box.