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

= 825cm^{3}

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)cm^{3}

= 683.84cm^{3}

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

^{3}

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

^{3}

^{3}

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