Question

The volume of the greatest right circular cone, which can be cut from a cube of side 4 cm is ______.

Answer 1

The volume of the greatest right circular cone, which can be cut from a cube of side 4 cm is `underlinebb((16π)/3 cm^3)`.

Explanation:

Given: Cube of side 4 cm; we must find the maximum volume of a right circular cone that can be cut from it.

Step wise calculation:

1. To maximize a right circular cone inside the cube, take its base as the largest circle that fits on one face circle inscribed in a square of side 4.

So base radius r = `4/2` = 2 cm and height h = side of cube = 4 cm.

2. Volume of a cone:

`V = (1/3)π r^2h`

3. Substitute r = 2 and h = 4:

`V = (1/3)·π·(2^2)·4` 

= `(1/3)·π·4·4`

= `(16/3) π cm^3`

4. Decimal value: 

`V ≈ (16/3)·3.14159 ≈ 16.76  cm^3`

The greatest right circular cone that can be cut from a cube of side 4 cm has volume `(16π)/3 cm^3` (≈ 16.76 cm³).