Question

The figure consists of 2 cylinders, the inner cylinder is a solid cylinder whose radius is r and the outer cylinder is a hollow cylinder whose radius is R and height is h, the volume of fluid it can hold is:

• A. $\pi r^{2}h$
• B. $\pi R^{2}h$
• C. $\pi (R^2-r^2)h$
• D. $\pi (R^2+r^2)h$

Answer 1

The correct option is C

$\pi (R^2-r^2)h$

The inner cylinder is solid whereas the outer is hollow. If the inner cylinder was not there, then the volume of fluid the outer cylinder can hold would be $\pi R^{2}h$ but since the inner cylinder is solid and is occupying some space, it is limiting the volume of the outer cylinder.

So, the volume of fluid the given shape can hold is the difference in volume of the outer and inner cylinders.

Volume = $\pi (R^2-r^2)h$