SSC CGL 16 Aug 2015 Shift 2 Paper

Radius of cylindrical vessel = r cm. (let).
Volume of conical piece of iron = $\frac{1}{3}\mathit{\pi }{\mathit{R}}^2\mathit{h}$
= $\left(\frac{1}{3}\mathit{\pi }\times 14\times 14\times 30\right)$ cu. cm.
Volume of raised water
= $\mathit{\pi }{\mathit{r}}^2$ × 6.4 cu. cm.
∴ $\mathit{\pi }{\mathit{r}}^2$ × 6.4 = $\frac{1}{3}$ π × 14 × 14 × 30
⇒ ${\mathit{r}}^2$ = $\frac{14\times 14\times 10}{6.4}$
⇒ ${\mathit{r}}^2$ = $\frac{{14}^2\times {10}^2}{8^2}$
⇒ r = $\frac{14\times 10}{8}$
⇒ 2r = $\frac{2\times 14\times 10}{8}$
= 35 cm = diameter