Question

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.​

Answer 1

Answer:

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Correct option is

B

1130400cm

3

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

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