Mathematics Lab Activity-15 Class IX | Surface Area & Volume

 Lab Activity-15 Class iX

Mathematics Lab Activities on Surface area and volume for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 11  surface area & volume

Activity - 15

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.

Procedure:

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

Figure 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].

Figure 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].

Figure 3

4. Fill the cone with sand (or salt) and pour it twice into the hemisphere. The hemisphere is completely filled with sand.
Therefore, volume of cone =1/2 volume of hemisphere.

5. Fill the cone with sand (or salt ) and pour it thrice into the cylinder. The cylinder is completely filled with sand.
Therefore, volume of cone =1/3volume of cylinder.

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

Observations

Radius of cone = Radius of Hemi-Sphere = Radius of Cylinder = r

Height of the cone = Height of cylinder = r

Volume of cone = (1/3) πr² x h = (1/3) πr² x r = (1/3) πr³.

Volume of Hemi-Sphere = (2/3)πr³.

Volume of Cylinder = πr² h

Volume of cone : Volume of hemisphere : Volume of cylinder 

= (1/3) πr³ : (2/3)πr³ : πr² h

= 1/3 : 2/3 : 1

Multiply all by 3 we get

= 1 : 2 : 3 

Result : 

.If cone, hemi-sphere and cylinder are of equal radius and equal height then the ratio of their volumes is given by 1 : 2 : 3

Applications

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.

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