The radius and height of a cylinder area in the ratio $$7:2$$. If the volume of the cylinder is $$8316\ cm^{3}$$, find the surface area of cylinder.
Given that radius and height of a cylinder are in the ratio $$7:2$$
Hence radius / height $$=7/2$$
$$r=(7/2)h$$
We know that the volume of the cylinder $$=\pi r^{2}h$$
So,
$$8316=22/7\times (7/2)h\times (7/2)h\times h$$
$$h^{3}=216$$
$$h=6\ cm$$
Therefore $$r=(7/2)\times 6=21\ cm$$
We know that total surface area of cylinder $$=2\pi r(r+h)$$
So,
Total surface area $$=2\times 22/7\times 21(21+6)$$
Total surface area $$=3564\ cm^{2}$$