Question

The height and the radius of the base of a cylinder are in the ratio $3:1$. If its volume is $1029$ $\pi c{m}^3$; find its total surface area.

• A. $1232$ $c{m}^2$
• B. $1200$ $c{m}^2$
• C. $1230$ $c{m}^2$
• D. $1233$ $c{m}^2$

Answer 1

The correct option is A $1232$ $c{m}^2$

Let height $=3x$, radius$=1x$
Volume of cylinder $=\pi r^{2}h=1029\pi$
$\Rightarrow x^2.3x=1029$

$\Rightarrow 3.x^3=1029$
$\Rightarrow x=7$
Height $=21$, radius $=7$
Total surface area $=2\pi r(r+h)c{m}^2=2\pi \left(7\right)(7+21)=1232c{m}^2$