Question

An oxygen cylinder is in the form of a right circular cylinder with a cone at one end and a hemisphere at the other end. Their common radius is r and height of cylindrical part is H cm and that of conical part is h cm. Express the volume V in terms of H, h & r

• A. $V=\frac{\pi r^2}{3}(h+H+2r)$
• B. $V=\frac{\pi r^2}{3}(h+2H+2r)$
• C. $V=\frac{\pi r^2}{3}(h+3H+4r)$
• D. $V=\frac{\pi r^2}{3}(h+3H+2r)$

Answer 1

The correct option is D $V=\frac{\pi r^2}{3}(h+3H+2r)$

Reqd volume $=$ volume of (cone+cylinder+ hemisphere)
$=\frac{1}{3}\pi r^{2}h+\pi r^{2}H+\frac{2}{3}\pi r^3$
$=\frac{\pi r^2}{3}(h+3H+2r)$