Question

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

Answer 1

Given: The edge of cube = 9 cm

⇒This will be the altitude of the cone.

Now,

The radius of circular cone will be $\frac{9}{2}$ = 4.5 cm.

As, we know that,
The volume of cone is given by formula:

$V=\frac{1}{3}\pi R^{2}H$

where,

R is the radius and H the altitude of cone.

Also, we are asked for the largest cone, its volume must be equal or less than the volume of cube.

$V=\frac{1}{3}\pi R^{2}H$

$=\frac{1}{3}\pi (4.5{)}^2\times 9$

$=\frac{1}{3}\pi \times 20.25\times 9$

$=\frac{1}{3}\times \frac{22}{7}\times 20.25\times 9=190.92c{m}^3$

Required volume is 190.92 cm³