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 bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

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Solution

We have to find the remaining volume of water left in the cylinder when the solid is inserted into it. The solid is a hemisphere surmounted by a cone.

Radius of cone, cylinder and hemisphere

Height of cone

Height of the cylinder

So the remaining volume of water left in the cylinder when the solid is inserted into it,

Put the values to get,

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A solid consisting of a right circular cone of height $120 c m$ and radius $60 c m$ standing on a hemisphere of radius $60 c m$ is placed upright in a right circular cylinder full of water such that it touches the bottoms. Find the volume of water left in the cylinder, if the radius of the cylinder is $60 c m$ and its height is $180 c m$ .

Q. Question 7
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.

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.

Q. A solid consisting of a right cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is

60 c m

and its height is

180 c m

, the radius of the hemisphere is

60 c m

and height of the cone is

120 c m

, assuming that the hemisphere and the cone have common base.

Q. A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .

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