Question

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

Answer 1

Sum of radius and height of a cylinder = 37 m

Let r be the radius and h be the height, then, r + h = 37 m

Total surface area of a solid cylinder = 1628 $m^2$

We know that total surface area of the cylinder $=2\pi rh+2\pi r^2=2\pi r(h+r)$

$\therefore 2\pi$ r (h + r) = 1628

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

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

But r + h = 37

$\therefore$ h= 37-r = 37 -7 = 30 m

Now volume = $\pi r^2$ h

=$\frac{22}{7}\times 7\times 7\times 30m^3=4620m^3$