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Question

A cylindrical bucket of height 10 cm and radius 5 cm is overturned to form a conical heap of sand of radius 5 cm. Find the height of the cone.

A
40 cm
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B
10 cm
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C
30 cm
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D
20 cm
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Solution

The correct option is C 30 cm
Given, the cylindrical bucket is overturned to form a conical heap of sand.

So, volume of the cylinder = volume of cone formed

Volume of cylinder =πr2h =227×52×10 =55007 cm2

Volume of cone=13πr2h

Volume of cylinder = Volume of cone

55007=13πr2h
55007=13×227×52×h
h=30 cm
Therefore, the height of the cone is 30 cm.

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