Question

The sum of the radius of the base and height of a solid cylinder is $37$$cm.$ If the total surface area is $1628{cm}^2,$ find the volume of the cylinder.

• A. 4616 $c{m}^3$
  
• B. 4650 $c{m}^3$
• C. 4110 $c{m}^3$
• D. 4220 $c{m}^3$

Answer 1

Answer: (A)

4616 $c{m}^3$

let the radius = $r$

let height = $h$

$r+h=37,h=37-r$

$TSA=2\pi rh+2\pi r^2=1628c{m}^2$

$2\pi r(37-r)+2\pi r^2=1628c{m}^2$

$2\pi \left(37r\right)=1628c{m}^2$

$r=7$

volume= $\pi r^{2}h=\pi 49(37-7)$

$=4615.8c{m}^3$