Question

A pyramid with volume 40 cubic inches has a rectangular base. If the length of the base is doubled, the width tripled and the height increased by 50%, what is the volume of the new pyramid, in cubic inches

Answer 1

`26.666666667`

Explanation:

To find the volume of a pyramid, you can use the formula:

Volume = (1/3) * base area * height

If the base is a rectangle, the base area is calculated by multiplying the length by the width.

Let's call the original length "L", the original width "W", and the original height "H".

The volume of the original pyramid is:

(1/3) * L * W * H = 40 cubic inches

If the length of the base is doubled, the new length is 2L.

The width is tripled, so the new width is 3W.

The height is increased by 50%, so the new height is 1.5H.

The volume of the new pyramid is:

(1/3) * (2L) * (3W) * (1.5H) = (2/3) * L * W * H = (2/3) * 40 cubic inches = 26.666666667 cubic inches.

So the volume of the new pyramid is approximately 26.666666667 cubic inches.