A right circular cylinder's height increases by 96% while its radius decreases by 25%. What is the approximate percentage change in its volume? Select the nearest integer.

Step-by-step solution

1. 1

   Define Original Volume

   The formula for the volume of a right circular cylinder is π times the square of the radius times the height.

   $$V = πr²h$$
2. 2

   Calculate New Dimensions

   The height increases by 96%, so the new height is 1 + 0.96 times the original height. The radius decreases by 25%, so the new radius is 1 - 0.25 times the original radius.

   $$h' = h(1 + percentage_increase) ; r' = r(1 - percentage_decrease)$$
3. 3

   Calculate New Volume

   Substitute the new height and new radius into the volume formula.

   $$V' = π(r')²h'$$
4. 4

   Calculate Percentage Change

   The percentage change is the difference between the new and original volume, divided by the original volume, multiplied by 100.

   $$\text{Percentage Change}\ = ((V' - V) / V) * 100$$