Question

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m₃. Find the ratio of its diameter to its height. 

(a) 3 : 7 

(b) 7 : 3 

(c) 6 : 7 

(d) 7 : 6

Answer 1

(b) 7 : 3

\(\frac{\text{Volume}}{\text{Curved Surface Area}}\) = \(\frac{πr^2h}{2πrh} = \frac{924}{264}\)

⇒ \(\frac{r}{2}=\frac{7}{2}\) ⇒ r = 7 m

and 2πrh = 264 ⇒ h = \(264\times\frac{7}{22}\times\frac12\times\frac17\) = 6 m

∴ Required ratio = \(\frac{2r}{h}=\frac{14}{6}\) = 7 : 3.