A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
Here, the volume of water left will be = Volume of cylinder – Volume of solid
Radius of cone = 60 cm,
Height of cone = 120 cm
Radius of cylinder = 60 cm
Height of cylinder = 180 cm
Radius of hemisphere = 60 cm
Total volume of solid = Volume of Cone + Volume of hemisphere
Volume of cone = π×122×103cm3
= 144 × 103π cm3
Total volume of solid = 144 × 103π cm3 - (2/3) × π × 103 cm3
Volume of hemisphere = (2/3) × π × 103 cm3
Volume of cylinder = π × 602 × 180 = 648000
= 648 × 103 π cm3
Volume of water left will be = Volume of cylinder – Volume of solid
= (648-288) × 103 × π = 1.131 m3