Question

The volume $V$ of a circular cylinder of radius $r$ and altitude $h$ is given by the formula $V=\pi r^{2}h$. Which if any, of the following statements is true?

• A. If both r and h are doubled, $V$ is doubled
• B. If $r$ is increased by $2$, $V$ is increased by $4$.
• C. If $r$ is doubled and $h$ is halved, $V$ remains the same.
• D. If $r$ is doubled and $h$ is divided by $4$, $V$ remains the same.
• E. None of these

Answer 1

The correct option is D If $r$ is doubled and $h$ is divided by $4$, $V$ remains the same.

Given, $V=\pi r^{2}h$
If $r$ and $h$ are doubled then volume $V$ will be eight times the original.
If $r$ is increased by $2$, then we cant have a relation between previous and present volume because $V$ is directly proportional to $r^2$.
If $r$ doubled and $h$ is halved then volume $V$ will be twice the original.
If $r$ doubled and $h$ is divided by $4$, then volume $V$ will be same as original.
So, the correct option is $D$.