Question

Find the volume of the cylinder whose total surface area is 1628 $c{m}^2$ and the circumference of its cross-section is 44 cm.

Answer 1

Total surface area of cylinder $=1628c{m}^2$
$2\pi r^2+2\pi rh=1628$ .........eq1
Circumference of its cross-section is $44cm$
$2\pi r=44$
$\therefore r=7$ ............eq2
So, from eq1 and eq 2
$2\pi r^2+2\pi rh=1628$
$2\pi 7^2+2\pi 7h=1628$
$\therefore h=30$
The volume of the cylinder
$V=\pi r^{2}h$
$V=\pi \times 7^2\times 30$
$V=4620c{m}^3$