Question

A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is ______.

Options

• `(pil^3)/(12)`

• `(pil^3)/(3)`

• `l^3(1 - pi/3)`

• `(pil^3)/(8)`

Answer 1

A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is `bbunderline((pil^3)/(12))`.

Explanation:

The base of the cone is a circle inscribed in the top face of the cube.

Diameter = l

Radius = `l/2`

The height of the cone equals the edge of the cube.

h = l

Volume of cone (V) = `1/3 pir^2h`

= `1/3pi(l/2)^2l`

= `1/3pi(l^2)/4l`

= `(pil^3)/12`