Page 82 - Mathematics Class - IX

OBSERVATIONS

The radius of cone = The height of the cone = ............... .
1
The volume of cone = × volume of ............
2
1
The volume of cone = × volume of .............
3
The volume of cone : The volume of a hemisphere = ............. : .............
The volume of cone : The volume of a cylinder = ............. : .............
Hence, the volume of cone : the volume of hemisphere : the volume of cylinder = ............. :.............

INFERENCE
1
It is concluded from point 5 of procedure that volume of cone = × volume of hemisphere.
2
1
Also, it is concluded from point 6 of procedure that volume of cone = × volume of cylinder.
3
Hence, volume of cone : volume of hemisphere: volume of cylinder = 1 : 2 : 3

EXTENDED TASK
1. Find the formula for the hemisphere from the formula of volume of cylinder.
2. To find the formula for the volume of cone from the formula of the volume of the cylinder.

APPLICATION

This relations is used in
1. Deriving the formula for volume of a cone and that of a hemisphere from the formula of volume of a cylinder.
2. Making packages of the similar material in containers of different shapes such as hemisphere, cylinder,
cone, etc.

Viva-Voce

1. What is the formula for the volume of a hemisphere?
2
Ans. pr 3
3

2. What is the formula for the volume of a right-circular cylinder?
Ans. pr h
2
3. What is the formula for the volume of a right-circular cone having height h and radius r?
1
Ans. pr h
2
3
4. What is the volume of a sphere?
4
Ans. pr 3
3

5. What is the relationships among the volumes of a right-circular cone, a hemisphere and a right-circular
cylinder of equal radii and equal heights?
Ans. The volumes are in the ratio 1 : 2 : 3.

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