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

The Correct Option is A

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).