A solid is in the form of right circular cone mounted on a hemisphere.The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. the solid is placed in a cylindrical tub,full of water,in such a way that the whole solid is submerged in water. if the radius of the cylindrical tub is 5 cm and its height is 10.5 cm,find the volume of water left in the cylindrical tub.
Answers
Question:
A solid is in the form of right circular cone mounted on a hemisphere.The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. the solid is placed in a cylindrical tub,full of water,in such a way that the whole solid is submerged in water. if the radius of the cylindrical tub is 5 cm and its height is 10.5 cm,find the volume of water left in the cylindrical tub.
Solution:
Given, radius of the hemisphere,
Now,
Since the solid is in the form of a right circular cone mounted on a hemisphere,
then, Radius of base of the cone = Radius of the hemisphere
→ radius of the base of the cone
Height of the cone,
So,
Volume of the solid = volume of the cone + volume of the hemisphere
→
→
→
Now, radius of the base of the cylindrical vessel,
Height of the cylindrical vessel,
∴ Volume of the water in the cylindrical vessel
Now, when the solid is completely submerged in the cylindrical vessel full of water,
then volume of the water displaced by the solid = volume of solid
Hence, volume of the water left in the vessel = volume of the water in the vessel - volume of solid
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