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 5:125:12, then the ratio of the total surface area of the cylinder to that of the cone is

Updated On: Jan 30, 2025
  • 3:13:1
  • 13:913:9
  • 17:917:9
  • 34:934:9
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The Correct Option is A

Solution and Explanation

Let radius of both be r = 5 and height be h =12 units
slant height of cone l = 52+122\sqrt{5^{2}+12^{2}} =169\sqrt{169} = 13 units
Total surface area of cylinder : Total surface area of cone = 2πr(r+h): πr(r+l)2 \pi r(r + h) :  \pi r(r + l)
10+245+13=3418\frac{10 + 24}{5 + 13}= \frac{34}{18}
⇒ 17:9
So, The correct option is (C).

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