Question

If the length and width of a rectangular solid are increased by 20% and the height is increased by 25%, by what percent is the volume of the solid increased?

(A) 21.67%
(B) 65%
(C) 80%
(D) 180%​

Answer 1

The volume of the rectangular solid can be calculated as length * width * height. When the length and width are increased by 20%, and the height is increased by 25%, the new dimensions would be:

length * 1.2 = 1.2 * length
width * 1.2 = 1.2 * width
height * 1.25 = 1.25 * height

The new volume would be:

(1.2 * length) * (1.2 * width) * (1.25 * height) = 1.44 * 1.44 * 1.25 * (length * width * height) = 2.401 * (length * width * height)

The original volume was (length * width * height), so the percent increase in volume is:

Percent increase = (2.401 * original volume - original volume) / original volume * 100 = (2.401 - 1) / 1 * 100 = 140%.

So, the answer is (D) 180%.