Question

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is $8316c{m}^3$, find the total surface area of the cylinder.

Answer 1

Ratio in radius and height of a cylinder =7 : 2

Let radius =7x

then height =2x

$\therefore$ Volume $=\pi r^{2}h=\frac{22}{7}\times 7x\times 7x\times 2x$

$=308x^3$

$\therefore 308x^3=8316$

$x^3=\frac{8316}{308}=27=(3{)}^3$

$\therefore x=3$

$\therefore$ Radius of cylinder $\left(r\right)=7x=7\times 3$

=21 cm

and height $\left(h\right)=2x=2\times 3=6cm$

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

$=2\times \frac{22}{7}\times 21(21+6)c{m}^2$

$=132\times 27c{m}^2$

$=3564c{m}^2$