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Question

A cone of maximum volume is carved out of a block of wood of size 20 cm x 10 cm x 10 cm. Find the volume of the remaining wood.

Solution
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Given that, a cone of maximum volume is to be carved out of a block of wood of size 20 cm×10 cm×10 cm.

The cone with maximum volume will have radius equal to half the length of the block and height equal to the height of the block.

Hence, radius of circular base =202=10 cm

And height of the cone =10 cm

Volume of the block =l×b×h=20×10×10

=2000 cm3

We know that,

Volume of a cone =13πr2h

13×3.14×10×10×10 [π=3.14]

=1046.66 cm3

Now,

Volume of the remaining wood = Volume of the block Volume of the cone

20001046.66=953.34 cm3


Hence, the volume of the remaining wood is 953.34 cm3.

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