GATE EC 2015 Set 3 — Question 8
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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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
Let cm be the radius of the circular sheet.
Area of the sheet .
Area of the sector removed of .
Remaining area .
When the remaining part is folded into a cone, its lateral surface area is equal to the remaining area of the sheet.
Lateral surface area of cone , where is the radius of the cone and is the slant height.
The slant height of the cone is equal to the radius of the circular sheet cm.
cm.
The height of the cone is given by cm.
The ratio of the radius to the height is .
The given range is 1.9 to 2.2.
Area of the sheet .
Area of the sector removed of .
Remaining area .
When the remaining part is folded into a cone, its lateral surface area is equal to the remaining area of the sheet.
Lateral surface area of cone , where is the radius of the cone and is the slant height.
The slant height of the cone is equal to the radius of the circular sheet cm.
cm.
The height of the cone is given by cm.
The ratio of the radius to the height is .
The given range is 1.9 to 2.2.
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