This is one of the important question from the cbse board exam point of view because in 2015 cbse board exam this question was asked. Question number 23 from RS Aggarwal book page number 811, exercise 17B, chapter volume and surface area of solid.

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# A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water, of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic meters.

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We have,

height of cone, h = 60 cm = 0.6 m

the base radius of cone, r = 30 cm = 0.3 m

the height of cylinder, H = 180 cm = 1.8 m

the base radius of the cylinder, R = 60 = 0.6 m

Now,

Volume of water left in the cylinder

Volume of the cone = 1/3 πr²h

= 1/3 π(0.3)²(0.6)

= 0.018π m³

volume of the cylinder = πR²H

= π(0.6)²(1.8)

= 0.648π m³

water left in cylinder = volume of the cylinder – volume of the cone

= 0.648π – 0.018π

= 1.98 m³

∴ volume of water left in the cylinder is 1.98 m³