GATE ME 2015 Set 2 — Question 8
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Question
From a circular sheet of paper of radius 30 cm, a sector of 10% area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is _______.
Correct answer
1.9 to 2.2
Solution
1.Let the radius of the circular sheet be cm.
2.Area of the original sheet . Since 10% is removed, the area of the remaining sector is .
3.When this sector is folded into a cone, the slant height of the cone is equal to the radius of the sheet: cm.
4.The area of the sector becomes the lateral surface area of the cone: , where is the radius of the cone base.
5. cm.
6.The height of the cone is .
7.The ratio of radius to height is .
8.The value lies within the range 1.9 to 2.2.
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