Question

A rectangular sheet of paper $22$cm long and $12$cm broad can be curved to form the lateral surface of a right circular cylinder in two ways. Taking $\pi =\frac{22}{7}$. Difference in the volumes of the two cylinders thus formed is

• A. $200$ c.c.
• B. $210$ c.c.
• C. $250$ c.c.
• D. $252$ c.c.

Answer 1

The correct option is B $210$ c.c.

Let radius of first cylinder be $x$ and that of second cylinder be $y$.
$2\pi x=22$
$2\pi y=12$

$\Rightarrow x=\frac{11}{\pi }$

$\Rightarrow y=\frac{6}{\pi }$

Difference between the volumes of the cylinders

$=[\pi r_1^2{h}_1-\pi r_2^2{h}_2]$

$=\pi \left[\right(\frac{11}{\pi }{)}^2\times 12-(\frac{6}{\pi }{)}^2\times 22]$

$=462-252$

$=210$ c.c.