Question

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

Answer 1

Let r and h be the radius and height of the cylinder, respectively.

It is given that, the ratio between the radius of base and the height of a cylinder is 2 : 3.

So, r = 2x and h = 3x, where x is constant

Volume of the cylinder = 1617 cm³

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

$\Rightarrow \frac{22}{7}\times {\left(2x\right)}^2\times 3x=1617$

$\Rightarrow \frac{22}{7}\times 4x^2\times 3x=1617$

$\Rightarrow x^3=\frac{1617\times 7}{12\times 22}={\left(\frac{7}{2}\right)}^3$

$\Rightarrow x=\frac{7}{2}\mathrm{cm}$

$\therefore r=2x=2\times \frac{7}{2}=7\mathrm{cm}$ and $h=3x=3\times \frac{7}{2}=\frac{21}{2}\mathrm{cm}$

Total surface area of the cylinder

$=2\mathrm{\pi }r\left(r+h\right)$

$=2\times \frac{22}{7}\times 7\times \left(7+\frac{21}{2}\right)$

$=44\times 17.5$

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

Thus, the total surface area of the cylinder is 770 cm².

The ratio between the radius of base and the height of a cylinder is 2 : 3. If its volume is 1617 cm³, the total surface area of the cylinder is ___770 cm²___.