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. ​

Answer 1

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 =

2

20

=10 cm

And height of the cone =10 cm

Volume of the block =l×b×h=20×10×10

=2000 cm

3

We know that,

Volume of a cone =

3

1

πr

2

h

⇒

3

1

×3.14×10×10×10 [π=3.14]

=1046.66 cm

3

Now,

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

⇒2000−1046.66=953.34 cm

3

Hence, the volume of the remaining wood is 953.34 cm

3

.