The radius of the base and the height of a cylinder are in the ratio 2 : 3. If its volume is 1617 cm3,
The radius of the base and the height of a cylinder are in the ratio 2 : 3. If its volume is 1617 cm3, find the total surface area of the cylinder.
Suppose that the radius of the base and the height of the cylinder are 2x cm and 3x cm, respectively.
Then $1617=\pi \mathrm{r}^{2} \mathrm{~h}=\frac{22}{7} \times(2 \mathrm{x})^{2} \times 3 \mathrm{x}$
$=\frac{22}{7} \times 12 \mathrm{x}^{3}$
$\Rightarrow \mathrm{x}^{3}=\frac{1617 \times 7}{22 \times 12}=42.875$
$\Rightarrow \mathrm{x}=\sqrt[3]{42.875}=3.5 \mathrm{~cm}$
Hence, radius = 7 cm; height of the cylinder = 10.5 cm
$\therefore$ Total surface area of the cylinder $=2 \pi r h+2 \pi r^{2}$
$=2 \times \frac{22}{7}(7 \times 10.5+7 \times 7) \mathrm{cm}^{2}$
$=\frac{44}{7} \times(73.5+49) \mathrm{cm}^{2}=770 \mathrm{~cm}^{2}$
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