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1. 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, 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

Solution:

Let their radius and height be 5x and 12x respectively
Slant height of the cone,

l = \sqrt{{(5 x)}^{2} + {(12 x)}^{2}} = 13 x

\begin{aligned} \frac{Total surface area of cylinder}{Total surface area of cone} \\ = \frac{2 π r (h + r)}{π r (l + r)} \\ = \frac{2 (h + r)}{(l + r)} \\ = \frac{2 \times (12 x + 5 x)}{(13 x + 5 x)} \\ = \frac{34 x}{18 x} \\ = \frac{17}{9} O r 17 : 9 \end{aligned}

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