A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

Radius of cylinder, R = 11 cm and height, H = 9 cm

Radius of cone, r = 10 cm and height, h = 8 cm

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

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

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

= $$(\frac{22}{7})[(11^2 \times 9)-(\frac{1}{3} \times 10^2 \times 8)]$$

= $$(\frac{22}{7})(1089-\frac{800}{3})$$

= $$\frac{22}{7} \times \frac{2467}{3}$$

$$\approx 2584.48$$ $$cm^3$$

=> Ans - (B)