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SURFACE AREAS

AND VOLUMES

  • Sum based on Cone and Hemisphere

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1 cm

Q. A solid is in the shape of a cone standing on a hemisphere

with both their radii being equal to 1 cm and the height of the

cone is equal to its radius. Find the volume of the solid in terms

of π.

Volume of solid =

The entire solid is made up

of a cone and a hemisphere

What is the formula to find volume of a hemisphere?

What is the formula to find volume of a cone?

Volume of cone (V1) +

Volume of hemisphere (V2)

 

 

Sol.

1 cm

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Volume of hemisphere (V2)

Now

Volume of cone (V1)

=

×

πr2h

h = r = 1cm.

=

×

π

×

1

×

1

×

1

=

π

Volume of hemisphere (V2)

=

×

πr3

=

×

π

×

1

×

1

×

1

=

π

1

3

1

3

1

3

2

3

2

3

2

3

cm3

cm3

Volume of cone (V1)

1 cm

1 cm

Volume of solid =

Volume of cone (V1) +

Volume of hemisphere (V2)

Sol.

Q. A solid is in the shape of a cone standing on a hemisphere

with both their radii being equal to 1 cm and the height of the

cone is equal to its radius. Find the volume of the solid in terms

of π.

 

 

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Volume of the solid

=

V1

=

π

+

π

+

V2

Volume of the solid

=

π cm3

1

3

2

3

 

 

=

3

π

+

2

π

=

3

3

π

=

π cm3

1 cm

1 cm

Sol.

Volume of solid =

Volume of cone (V1) +

Volume of hemisphere (V2)

Q. A solid is in the shape of a cone standing on a hemisphere

with both their radii being equal to 1 cm and the height of the

cone is equal to its radius. Find the volume of the solid in terms

of π.