The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672 m2, what is the volume of the cylinder ?

Answer: Option A

Let the radius of the cylinder be r and height be h
Then, r + h = 19
Again, total surface area of cylinder = $$\left(2\pi rh+2\pi r^2\right)$$
Now,
$$\begin{array}{rl}& 2\pi r\left(h+r\right)=1672\\ & \Rightarrow 2\pi r\times 19=1672\\ & \Rightarrow 38\pi r=1672\\ & \therefore \pi r=\frac{1672}{38}=44m\\ & \therefore r=\frac{44\times 7}{22}=14m\end{array}$$
∴ Height = 19 - 14 = 5 m
Volume of cylinder :
$$\begin{array}{rl}& =\pi r^{2}h\\ & =\frac{22}{7}\times 14\times 14\times 5\\ & =22\times 2\times 14\times 5\\ & =3080m^3\end{array}$$