Question

The sum of the height and the radius of a solid cylinder is $35cm$ and its total surface area is $3080c{m}^2$; find the volume of the cylinder.

• A. $12,936cu.cm$
• B. $12,933cu.cm$
• C. $12,930cu.cm$
• D. $12,900cu.cm$

Answer 1

Answer: (A)

$12,936cu.cm$

Given, $r+h=35$
Total surface area $=3080c{m}^2$
$\therefore 2\pi r(r+h)=3080$
$\Rightarrow r=\frac{3080}{2\pi \left(35\right)}=14.013$
$\Rightarrow h+14=35$
$\Rightarrow h=21$
$\therefore$ volume of cylinder $=\pi r^{2}h$
$=\pi \left(14{)}^2\right(21)$

$=12,936$ cu. cm