Question

The curved surface area of a cylinder is $264m^2$ and its volume is $924m^3$ Tile ratio of its diameter to its height is

• A. $7:6$
• B. $6:7$
• C. $3:7$
• D. $7:3$

Answer 1

The correct option is D $7:3$

Surface Area of a Cylinder of Radius "r" and height "h" $ = 2\pi

rh = 264 {m}^{2} $ --- (1)

Volume of a Cylinder of Radius "r" and height "h" $ = \pi { r }^{

2 }h = 924 {m}^{3} $ ----- (2)

Dividing 2 by 1,

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

$=>\frac{r}{2}=\frac{7}{2}$

$=>r=7m$

From equation (1), $2\pi rh=2\times \frac{22}{7}\times 7\times h=264$

$=>h=6m$

Hence, required ratio $=\frac{Diameter}{Height}=\frac{14}{6}=\frac{7}{3}=7:3$