Question

The radius of the base and the height of a cylinder are in the ratio of 2:3. If its volume is $12936c{m}^3$, then find the total surface area of the cylinder.
(4 marks)

Answer 1

Since the ratio of the radius and the height is 2:3, we can assume the radius (r) = 2$x$ and the height (h) = 3$x$
(0.5 marks)

The volume of a cylinder is given by:
$\pi r^{2}h=12936c{m}^3$

$\Rightarrow \frac{22}{7}\left(2x{)}^2\right(3x)=12936$

$\Rightarrow x^3=\frac{12936\times 7}{22\times 2\times 3}$

$\Rightarrow x=\sqrt[3]{3343}$

$\Rightarrow x=7$
(1.5 marks)

Hence, the radius of the base = $2\times 7=14cm$, and
the height of the base = $3\times 7=21cm$.
(1 mark)

$\therefore$ Total surface area of the cylinder

= $2\pi r(r+h)$

= $2\pi \left(14\right)(14+21)$

$=2\times \frac{22}{7}\times 14\times \left(35\right)=3080c{m}^2$
(1 mark)