036 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
Take T = 3.14)
Step-by-step explanation:
Given, Radius of cone=60cm
Height of cone=120cm
Radius of hemisphere=60cm
Radius of cylinder=60cm
Height of cylinder=180cm
Volume of cone is,
=
3
1
πr
2
h
=
3
1
π×660
2
×120
=14000πcm
3
Volume of hemisphere is,
=
3
4
πr
3
h
=
3
2
π60
3
h
=144000πcm
3
Volume of cylinder is,
=πr
2
h
=π×60
2
×180
=648000πcm
3
Volume of water left in cylinder is
=πr
2
h−
3
1
πr
2
h−
3
4
πr
3
h
=(648000−288000)π
=360000π
=1130400cm
3
solution