Question

The ratio of the radius and height of a cylinder is $2:3$. If its volume is $12936c{m}^3$, find the total surface area of the cylinder.

Answer 1

The ratio of the radius and height of a cylinder $=2:3$
Let the radius of the cylinder be $2x$ and the height of the cylinder be $3x$.
Volume of the cylinder $=12936c{m}^3$
$\because$ Volume of a cylinder $=\pi r^{2}h$
$\therefore 12936=\frac{22}{7}\times (2x{)}^2\times 3x$
$\Rightarrow 12936=\frac{22}{7}\times 4x^2\times 3x\Rightarrow 12936=\frac{264}{7}{x}^3\Rightarrow x^3=\frac{12936\times 7}{264}=49\times 7\Rightarrow x^3=7\times 7\times 7=(7{)}^3\Rightarrow x^3=(7{)}^3\therefore x=7$
So, radius $2x=2\times 7=14cm$ and height $=3x=3\times 7=21cm$
The total surface area of the cylinder$=2\pi r(r+h)$
$=2\times \frac{22}{7}\times 14(14+21)=\frac{44\times 14}{7}\times 35=44\times 14\times 5=3080c{m}^2$