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

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

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 $=\frac{20}{2}=10cm$

And height of the cone $=10cm$

Volume of the block $=l\times b\times h=20\times 10\times 10$

$=2000c{m}^3$

We know that,

Volume of a cone $=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{1}{3}\times 3.14\times 10\times 10\times 10$ $[\pi =3.14]$

$=1046.66c{m}^3$

Now,

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

$\Rightarrow 2000-1046.66=953.34c{m}^3$

Hence, the volume of the remaining wood is $953.34c{m}^3$.