Question

A largest possible cuboid is carved out of a wooden cylinder. The cylinder has a base radius of $14\sqrt{2}$ cm and a height of $16$ cm. Find the volume of wood wasted (in $c{m}^3$) .(Take $\pi =\frac{22}{7}$)

• A. $6524$
• B. $6838$
• C. $7168$
• D. $7456$

Answer 1

The correct option is C $7168$

Given that:

Base radius $=14\sqrt{2}cm$

Height $=16cm$

To find:

Volume of wasted wood$=?$

Solution:

For largest possible cuboid, the base of the carved cuboid must be a square.

Let $a$ be the side of the square.

then $a^2+a^2=(2\times 14\sqrt{2}{)}^2$

or, $2a^2=1568$

or, $a^2=784$

or, $a=28cm$

Now,

Volume of wasted wood$=$ Volume of Cylinder $-$ Volume of largest possible cuboid

$=\pi r^{2}h-a\times a\times h$

$=\frac{22}{7}\times (14\sqrt{2}{)}^2\times 16c{m}^3-28\times 28\times 16c{m}^3$

$=(19712-12544)c{m}^3$

$=7168c{m}^3$

Volume of wasted wood$=7168c{m}^3$

Hence, C is the correct option.