An edge of a cube measures 10 cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone is:

1. 260 cm³

2. 260.9 cm³

3. 261.9 cm³

4. 262.7 cm³

Edge of a cube = 10 cm

Volume = side³ = 10³ = 1000 cm³.

Cone of maximum size is carved out as shown in figure,

Diameter of the cone cut out from it = 10 cm

Radius, r = $\dfrac{\text{diameter}}{2} = \dfrac{10}{2}$ = 5 cm

Height, h = 10 cm

Volume of cone = $\dfrac{1}{3}$ πr²h

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 5^2 \times 10 \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times 25 \times 10 \\[1em] = \dfrac{5500}{21} \\[1em] = 261.9 \text{ cm}^3.$

Hence, option 3 is the correct option.