Question 88

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

Solution

Side of cube = 6 cm

Height of cone = 6 cm and radius of cone = $$\frac{6}{2} = 3$$ cm

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

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

= $$(6)^3 - [\frac{1}{3} \times \frac{22}{7} \times (3)^2 \times 6]$$

= $$216 - (\frac{22 \times 18}{7})$$

= $$216 - 56.58$$

= $$159.42$$ $$cm^3$$

=> Ans - (A)

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