Question

The ratio between the radius of the base and the height of a cylinder is 2:3. Find the total surface area of the cylinder, if its volume is 1617 $c{m}^2$.

Answer 1

Ratio between radius and height of a cylinder = 2:3

Volume = 1617 $c{m}^3$

Let radius (r) = 2x

Then height (h) = 3x

$\therefore Volume=\pi r^2$ h

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

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

$\Rightarrow x^3=\frac{1617\times 7}{22\times 4\times 3}=\frac{343}{8}$

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

$\therefore x=\frac{7}{2}$

$\therefore$ Radius = 2x = 2 $\times \frac{7}{2}$ = 7 cm

and height = $3x=3\times \frac{7}{2}=\frac{21}{2}$ cm

$\therefore$ Total surface area = $2\pi$ r (h+r)

=$2\times \frac{22}{7}\times 7(\frac{21}{2}+7)c{m}^2$ = $44\times \left(\frac{21+14}{2}\right)=44\times \frac{35}{2}c{m}^2$ = 770 $c{m}^2$