Question

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

Answer 1

Ratio in radius and height of the cylinder = 2:3

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

$\Rightarrow \frac{264}{7}{x}^3=1617\Rightarrow x^3=\frac{1617\times 7}{264}$

$\Rightarrow x^3=\frac{49\times 7}{8}={\left(\frac{7}{2}\right)}^3$ $\therefore x=\frac{7}{2}$cm

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

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

Now total surface area = $2\pi$ r(h+r)

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

= $44\times \frac{35}{2}c{m}^2=770c{m}^2$