Question

The, sum of the radius of the base and the height of a solid cylinder is $37$ metres. If the total surface area of the cylinder be $1628$ sq. metres, its volume is :

• A. $3180m^3$
• B. $4620m^3$
• C. $5240m^3$
• D. None of these

Answer 1

Answer: (B)

$4620m^3$

Given $(r+h)=37m$____(i)

and $TSA=1628m^2$

$=2\pi r(r+4)$

substituting $(r+h)$ from (i) and $\pi =\frac{22}{7}$

$1628=2\times \frac{22}{7}\times r\times 37$

$\Rightarrow r=7m$

substituting r in (i) gives

$h=37-7=30m$

volume $=\pi r^{2}h$

$=\frac{22}{7}\times 7^2\times 30$

$=22\times 7\times 30$

$=4620m^3$