A solid right circular cone of radius 4 cm and height 7 cm is put inside a cylindrical vessel of radius 5 cm and height 8 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

Radius of cylinder, R = 5 cm and height, H = 8 cm

Radius of cone, r = 4 cm and height, h = 7 cm

Water required to fill the cylinder completely = Volume of cylinder - Volume of cone

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

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

= $$(\frac{22}{7})[(5^2 \times 8)-(\frac{1}{3} \times 4^2 \times 7)]$$

= $$(\frac{22}{7})(200-\frac{112}{3})$$

= $$\frac{22}{7} \times \frac{488}{3}$$

$$\approx 511.24$$ $$cm^3$$

=> Ans - (C)