Question

The volume of the largest right circular cone that can be cut out from a cube of edge $4.2cm$ is:

• A. $9.7c{m}^3$
• B. $77.6c{m}^3$
• C. $19.404c{m}^3$
• D. $19.4c{m}^3$

Answer 1

Answer: (C)

$19.404c{m}^3$

Edge of the cube $=4.2$ cm

Let the radius of base of the cone be $r$ cm and height be $h$ cm.

The base of largest cone that can touch all the edges of the base of the cube and its height, is same on the edge of the cube.

Therefore,

$2r=4.2cmr=2.1cmh=4.2cm$

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

$=\frac{1}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 4.2=19.404{cm}^3$