Class 09 To find the relationship among the volumes of a right circular cone, a hemisphere and a right circular cylinder of equal radii and equal heights.

 

Activity 29

OBJECTIVE                                                                     

To find the relationship among the volumes of a right circular cone, a hemisphere and a right circular cylinder of equal radii and equal heights.

 MATERIAL REQUIRED

 Cardboard, acrylic sheet, cutter, a hollow ball, adhesive, marker, sand or salt.

 METHOD OF CONSTRUCTION

 1.   Take a hollow ball of radius, say, a units and cut this ball into two halves [see Fig. 1].

 2.    Make a cone of radius a and height a by cutting a sector of a circle of suitable radius using acrylic sheet and place it on the cardboard [see Fig. 2].

 3.   Make a cylinder of radius a and height a, by cutting a rectangular sheet of a suitable size. Stick it on the cardboard [see Fig. 3].

DEMONSTRATION

 1.   Fill the cone with sand (or salt) and pour it twice into the hemisphere. The hemisphere is completely filled with sand.

 1Therefore, volume of cone = ₂ volume of hemisphere.

 2.   Fill the cone with sand (or salt ) and pour it thrice into the cylinder. The cylinder is completely filled with sand.

 1Therefore, volume of cone = ₃ volume of cylinder.

 3. Volume of cone : Volume of hemisphere : Volume of cylinder = 1:2:3

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OBSERVATION
Radius of cone = Height of the cone  = ---------						.
Volume of cone	=		1		Volume of	.
	2
Volume of cone	=	1			Volume of ---------------	.
	3
Volume of cone : Volume of a hemisphere = --------						: ----------
Volume of cone : Volume of a cylinder = --------						: ----------
Volume of cone : Volume of hemisphere : Volume of cylinder = --------							:
---------- : ---------

 APPLICATION

 1.    This relationship is useful in obtaining the formula for the volume of a cone and that of a hemisphere/sphere from the formula of volume of a cylinder.

 2.    This relationship among the volumes can be used in making packages of the same material in containers of different shapes such as cone, hemisphere,cylinder.