Volume of Complex Solid Figure Containing Cone and Hemisphere

Rahul promised to give Ice-cream party to his friends.

He decides to serve ice-cream cone to every friend.

But due to sudden problem, he is running short of funds.

He is a smart boy, So he decides to buy empty ice-cream cone and fill them with ice-cream.

By this way, he finds that funds available with him will be sufficient.

But he don’t know how much quantity of ice-cream he requires.

And he doesn’t want to waste any ice-cream. So he wants to know exact amount of ice-cream.

Suddenly he realises that space any object occupies is known as volume of object.

Basically, to know the exact amount of ice-cream he needs to know volume of ice-cream cone

So he starts to turn pages of his math book.

There was a formula for cone’s volume.

There was also a formula for hemisphere’s volume.

But he fails to find any direct formula for volume of ice-cream cone.

Then he remembers the theory of complex shapes.

Mathematically, complex shape is combination of two or more simple shapes.

To find the volume of complex shape, we first find the volume of all the simple shapes.

Like in the case of ice cream cone, we first find the volume of hemisphere.

And then the cone.

After finding the volume of simple shapes,we add them to find volume of complex shape.

Like in this case volume of ice-cream comes out to be

After this rahul is able to find the amount of ice-cream he requires to fill ice-cream cone.

Revision

Volume of cone

Volume of hemisphere

Volume of ice-cream cone

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