Question

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

Answer 1

Let $r=2x$ and $h=3x.$

$V=\pi r^{2}h$

$⟹\frac{22}{7}\times \left(4x^2\right)\left(3x\right)=1617$

$⟹x^3=42.875$

$⟹x=3.5cm$

Hence, $r=7cm$ and $h=10.5cm$

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

$=2\times \frac{22}{7}\times 7\left(17.5\right)$

$=770c{m}^2$