The ratio between the radius of the base and the height of a cylinder is 2 : 3. If its volume is 1617 cm3,
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

Solution:

(d) 770 cm2
We have:
r: h = 2 : 3

$\Rightarrow \frac{r}{h}=\frac{2}{3}$

$\Rightarrow h=\frac{3}{2} r$

Now, volume $=1617 \mathrm{~cm}^{3}$

$\Rightarrow \pi r^{2} h=1617$

$\Rightarrow \frac{22}{7} \times r^{2} \times \frac{3}{2} r=1617$

$\Rightarrow r^{3}=\frac{1617 \times 14}{66}=343$

$\Rightarrow r=7 \mathrm{~cm}$

∴ h = 10.5 cm

Hence, total surface area $=2 \pi r h+2 \pi r^{2}$

$=\frac{22}{7}\left(2 \times 7 \times 10.5+2 \times 7^{2}\right)$

$=\frac{22}{7}(147+2 \times 49)$

$=\frac{22}{7} \times 245$

$=770 \mathrm{~cm}^{2}$