Question

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

Let, diameter of cone be edge of the square

∴ `l = square` cm

∴ h = `square` 4 cm

r = 2 cm

Volume of cone = `square`   ...........(Formula)

V = `1/3 π square^3 xx 4`

V = `square` cm³

Answer 1

1. Edge length of the cube `(l)`:

∴ `l` = \[\boxed{4}\] cm

2. Height of the cone (h):

The maximum height of the cone is equal to the edge of the cube.

∴ h = \[\boxed{4}\] cm

3. Formula for the volume of a cone:

Volume of cone = \[\boxed{\frac{1}{3} πr^2h}\]   ...........(Formula)

4. Substituting the values:

\[V = \frac{1}{3} π\boxed{2}^2 \times 4\]

5. Final calculation:

`V = 1/3 xx π xx 4 xx 4`

= `16/4 π  cm^3`

1. If keeping it in terms of π:

\[V = \boxed{\frac{16}{3}π} \phantom{.} cm^3\]

2. If substituting `π ≈ 22/7`:

`V = 16/3 xx 22/7`

= \[\frac{352}{21} ≈ \boxed{16.76} \phantom{.} cm^3\]