Question

if the radius of base and height of a right circular cone and a right circular cylinder are equal then the ratio of their volume is​

Answer 1

Let their radius and height be 5x and 12x respectively

Slant height of the cone,

$l = \sqrt{( {5x}^{2}) + ( {12x}^{2})} \\ = 13x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \frac{total \: surface \:area \: of \: cylinder }{total \: surface \: area \: of \: cone} \\ \\ = \frac{2\pi r(h + r)}{\pi r(l + r)} \\ \\ = \frac{2(h + r)}{(l + r)} \: \: \\ \\ = \frac{2 \times (12x + 5x)}{(13x + 5x)} \\ \\ = \frac{34x}{18x} \\ \\ = \frac{17}{9}$

or 17:9.