Question

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

• A. $4620cu.m$
• B. $4630cu.m$
• C. $4520cu.m$
• D. $4830cu.m$

Answer 1

Answer: (A)

$4620cu.m$

Let radius and base of cylinder be $r$ and $h$ respectively.

$\therefore$ $r+h=37$m, Now, TSA $=1628$$m^2$

$\Rightarrow 2\pi r(r+h)=1628m^2\Rightarrow 2\times \frac{22}{7}\times r\times 37=1628$

$\Rightarrow r=\frac{1628\times 7}{44\times 37}=7m$, Now $r+h=37\Rightarrow h=37-7=30m$

Volume $=$ $\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 30=4620m^3$