The radius of the base of a right circular cylinder is increased by 20%. By what per cent should its height be reduced so that its volume remains the same as before?

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& 20\%\to \frac{+1}{5}\\ & V=\pi R^{2}h\\ & R\to 5:6\\ & R^2\to 25:36\\ & \boxed{R^2\propto \frac{1}{h}}\text{ If volume same}\end{array}$$

$$\frac{11}{36}\times 100=30\frac{5}{9}\%$$