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 $5:12$, 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: (A)

$3:1$

Answer 2

Let radius of both be r = 5 and height be h =12 units
slant height of cone l = $\sqrt{5^{2}+12^{2}}$ =$\sqrt{169}$ = 13 units
Total surface area of cylinder : Total surface area of cone = $2 \pi r(r + h) : \pi r(r + l)$
⇒$\frac{10 + 24}{5 + 13}= \frac{34}{18}$
⇒ 17:9
So, The correct option is (C).