Question

A rectangular sheet of paper $22$cm long and $10$ cm broad can be curved to form the lateral surface area of a right circular cylinder in two ways. Then the difference between the volumes of the two cylinders thus formed is

• A. $200c{m}^3$
• B. $210c{m}^3$
• C. $250c{m}^3$
• D. $252c{m}^3$

Answer 1

Answer: (B)

$210c{m}^3$

(i) When breadth becomes the curved surface:
Height$=22$ cm
$2\pi r=10$
$\therefore r=\frac{5}{\pi }$ cm

Volume $=\pi r^{2}h=\pi \frac{25}{{\pi }^2}22=175c{m}^3$

(ii) When length becomes the curved surface:
Height$=10$ cm
$2\pi r=22$
$\therefore r=\frac{7}{2}$ cm

Volume $=\pi r^{2}h=\pi \frac{49}{4}10=385c{m}^3$

$\therefore$ Difference in 2 volumes $=385-175=210c{m}^3$