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Question

A solid right circular of radius 60 cm and height 20 cm is melted and recast into a right circular cone of height 3 times that of the cylinder.  Find the curved surface area of the cone in square cm correct up to two places of decimal.  (Use π=3.14)  [4 MARKS]


Solution

Formula: 1 Mark
Application: 1 Mark
Solution: 2 Marks

For cylinder:  radius = R cm, height = h cm
For cone: radius = r cm, height = H cm
According to question,
Volume of metal used for making cylinder and cone are equal.
πR2h=12πr2H(60)2×20=12r2×60 r=60 cm
Slant height of cone, l=r2+H2=(60)2+(60)2=7200=602m
Curved surface area of cone =πrl=3.14×60×62cm2=15983.86cm2

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