Describe how multiplying the height by 3/2 affects the volume of the pyramid.

Question

The square pyramid has a height of 14cm, and side lengths of 18cm and 12cm.

The volume is ___ times the original volume.

Answer 1

Volume = (1/3) * (Base length * base width) * height

vs.

New Volume = (1/3) * (Base length * base width) * 3/2*height

in which the 3 cancels out.

= (1/2) * (Base length * base width) * height

The ratio of the old volume to the new volume is then

1/3 divided by 1/2 = 1/3 * 2/1 = 2/3, or 2 to 3 ratio

In the case of the given pyramid, the old volume is (1/3)(14)(18)(12) = 1008

the new volume features a height of (3/2)(14) = 21, which is then

(1/3)(21)(18)(12) = 1512

1008/1512 = 336/504 = 112/168 = 56/84 = 28/42 = 4/6 = 2/3