A cone is hollowed out of a solid wooden cube of side 7 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

Side of cube = 7 cm

Height of cone = 7 cm and radius of cone = $$\frac{7}{2}$$ cm

Volume of remaining cube = Volume of cube - Volume of cone

= $$(a)^3 - \frac{1}{3} \pi r^2 h$$

= $$(7)^3 - \frac{1}{3} \times \frac{22}{7} \times (\frac{7}{2})^2 \times 7$$

= $$(7)^3 \times [1 - (\frac{1}{3} \times \frac{11}{7 \times 2})]$$

= $$(7)^3 \times [1 - \frac{11}{42}]$$

= $$343 \times (\frac{42 - 11}{42})$$

= $$\frac{49 \times 31}{6} = 253.17 cm^3$$