Question

The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm³, then its total surface area is
(a) 308 cm²
(b) 462 cm²
(c) 540 cm²
(d) 770 cm²

Answer 1

(d) 770 cm²
We have:
r: h = 2 : 3
$$\begin{gathered} \Rightarrow \frac{r}{h}=\frac{2}{3} \\ \Rightarrow h=\frac{3}{2}r \end{gathered}$$
Now, volume = 1617 cm³
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^{\mathit{2}}h\mathit{}=1617 \\ \Rightarrow \frac{22}{7}\times r^2\times \frac{3}{2}r\mathit{}=1617 \\ \Rightarrow r^3=\frac{1617\times 14}{66}=343 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

∴ h = 10.5 cm

$$\begin{gathered} \mathrm{Hence},\mathrm{total}\mathrm{surface}\mathrm{area}=2\mathrm{\pi }rh+2\mathrm{\pi }{r}^2 \\ =\frac{22}{7}(2\times 7\times 10.5+2\times 7^2) \\ =\frac{22}{7}\left(147+2\times 49\right) \\ =\frac{22}{7}\times 245 \\ =770{\mathrm{cm}}^2 \end{gathered}$$