Question

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio $5:12$ respectively, then the ratio of the total surface area of the cylinder to that of the cone is __________.

• A. $3:1$
• B. $13:9$
• C. $17:9$
• D. $34:9$

Answer 1

Answer: (C)

$17:9$

It is given that, $r:h=5:12$

Surface area of cylinder $A_1=2\pi rh+2\pi r^2$

And surface area of cone $A_2=\pi rl+\pi r^2$ (where $l=\sqrt{h^2+r^2}$)

$\frac{A_1}{A_2}=\frac{2\pi r(h+r)}{\pi r(\sqrt{h^2+r^2}+r)}$

Put $h=12x$ and $r=5x$

$\frac{A_1}{A_2}=\frac{2(12+5)x}{(13+5)x}=\frac{17}{9}$