Question

The curved surface area of a cylindrical pillar is $264m^2$ and its volume is $924m^3$. Then find the ratio of its diameter to its height.

• A. $\frac{11}{3}$
• B. $\frac{7}{3}$
• C. $\frac{5}{3}$
• D. $\frac{13}{3}$

Answer 1

The correct option is B $\frac{7}{3}$

Curved surface area of cylinder = $264m^2$
or, $2\pi rh=264m^2$ ...................(i)

Volume of cylinder = $924m^3$

or, $\pi r^{2}h=924m^3$ .....................(ii)

Dividing (i) by (ii), we get

$\frac{2\pi rh}{\pi r^{2}h}=\frac{264}{924}$

or, $\frac{2}{r}=\frac{264}{924}$

or, $r=\frac{924\times 2}{264}=7m$

Now, $2\pi rh=264$ [from equation (i)]

$\Rightarrow h=\frac{264}{2\times \pi \times 7}=6m$

$\therefore$ Required ratio $=\frac{Diameter}{Height}=\frac{2r}{h}=\frac{2\times 7}{6}=\frac{7}{3}$