Volumes Practice Test 1

Here, r = $\frac{\mathit{h}}{2}$
∴ h = 2r
Since, $\mathit{\pi }{\mathit{r}}^2+2\mathit{\pi }\mathit{r}\mathit{h}$ = 616
⇒ πr (r + 2h) = 616
⇒ πr (r + 2 × 2r) = 616
⇒ $\mathit{\pi }\times 5{\mathit{r}}^2$ = 616
∴ ${\mathit{r}}^2$ = $\frac{616\times 7}{22\times 5}$
∴ r = $\frac{14}{\sqrt{5}}$ cm
Then, h = 2r = 2 × $\frac{14}{\sqrt{5}}$ = $\frac{28}{\sqrt{5}}$ cm
Hence, Volume of the cylinder = $\frac{22}{7}\times {\left(\frac{14}{\sqrt{5}}\right)}^2\times \frac{28}{\sqrt{5}}$ = $\frac{17248\sqrt{5}}{25}$
= $\frac{17248\times 2.23}{25}$ = $\frac{38463.04}{25}$ = 1538 c.c.