The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³ $$\left( {{\text{Taking }}\pi = \frac{{22}}{7}} \right).$$    Find the ratio of its diameter to its height

Solution (By Examveda Team)

$$\eqalign{ & 2\pi rh = 264{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \pi {r^2}h = 924{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{On dividing}}:\frac{{2\pi rh}}{{\pi {r^2}h}} = \frac{{264}}{{924}} \cr & \frac{2}{r} = \frac{{264}}{{924}} \cr & r = \frac{{924 \times 2}}{{264}} \cr & r = 7{\text{ cm}} \cr & {\text{Diameter}} = 2r = 2 \times 7 = 14{\text{ cm}} \cr & {\text{Putting, }}r = 7{\text{ in equation }}\left( {\text{i}} \right) \cr & 2\pi rh = 264 \cr & h = \frac{{264 \times 7}}{{2 \times 22 \times 7}} \cr & h = 6{\text{ cm}} \cr & {\text{Required ratio}} = \frac{{2r}}{h} = \frac{{14}}{6} = \frac{7}{3} \cr} $$