Question

A cyilndrical tub of radius 5 cm and length 9.8 cm is full of water. A solid is in the form of a right circular cone moutned on a hemisphere and is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub

Answer 1

volume of left water in the tub=volume of full water in the tub-volume of poured water from the tub

but we know volume of poured water from the tub=volume of solid object immersed in the tub=volume of cone+volume of hemisphere
=pi. (r)^2.h/3+2/3pi. (r)^3
=1/3.pi.(r)^2{h+2r)=1/3x(22/7)x(7/2)x(7/2)x12
=154cm^3

now get volume of water initially in the tub=pi. (r)^2.h=(22/7)x (5) x (5) x(9.8)
=770cm^3

now water left =770-154=616cm^3