Question
A Solid is in the form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 3.5 cm and height of the cone is 4 cm . The solid is placed in a cylindrical vessel , full of water , in such a way that the whole solid is submerged in water. If the radius of cylindrical vessel is 5 cm and its height is 10.5 cm . Find the volume of water left in the cylindrical vessel
Hint:
Volume of hemisphere
The correct answer is: 683.84cm3
Explanation:
- We have given a Solid is in the form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 3.5 cm and height of the cone is 4 cm . The solid is placed in a cylindrical vessel , full of water , in such a way that the whole solid is submerged in water. If the radius of cylindrical vessel is 5 cm and its height is 10.5 cm
- We have to find volume of water left in the cylindrical vessel.
Step 1 of 1:
We have given radius of the hemisphere is 3.5cm
Now the solids is in the form of a right circular cone mounted on a hemisphere, then radius of the base of the cone will be equal to radius of the hemisphere.
Radius of the base of the cone is
Height of the cone is
So,
Volume of the solid = volume of the cone + volume of hemisphere.
So,
= 141.109
Now the radius of the base of the cylindrical vessel is 5cm
Height of the cylindrical vessel is 10.5cm
So, Volume of the water in the cylindrical vessel will be
= 825cm3
Now, when the solid is completely submerged in the cylindrical vessel full of water,
The
Volume of the water left in the vessel = volume of the water in the vessel – volume of solid
= (825 - 141.16)cm3
= 683.84cm3
Now the radius of the base of the cylindrical vessel is 5cm
Height of the cylindrical vessel is 10.5cm
So, Volume of the water in the cylindrical vessel will be
Now, when the solid is completely submerged in the cylindrical vessel full of water,
The
Volume of the water left in the vessel = volume of the water in the vessel – volume of solid
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