Page 81 - Mathematics Class - IX

ACTIVITY 5.4

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.

MATERIALS REQUIRED

Cardboard Hollow ball Marker Adhesive
Geometry box Cutter Sand or salt Acrylic sheets

PRE-REQUISITE KNOWLEDGE

1. Concept of cone and its properties. 3. Concept of sphere, hemisphere and its properties.
2. Concept of cylinder and its properties.

THEORY
1. For cone and its properties, refer to Activity 5.1.
2. For concept of cylinder, refer to Activity 5.2.

3. A sphere is three-dimensional figure (solid figure) which is made up of all points in the space, which lie
at a constant distance, from a fixed point called the centre of the sphere and the constant distance is called
its radius.

4. Hemisphere: Half portion of a sphere.

PROCEDURE
1. Take a hollow ball of radius x units and cut it into two halves (Fig. (a)).
2. Take an acrylic sheet and cut it to get right-circular cone of radius x units and height x units (Fig. (b)).

3. Take a rectangular piece of acrylic sheet and cut it to get a right-circular cylinder of radius x units and height
x units (Fig. (c)).

x

x x x x
x

x x x x

Fig. (a) Fig. (b) Fig. (c)

4. Place hemisphere, right circular cone and right circular cylinder on the cardboard.
5. Let the cone be filled with sand or salt and pour it twice into the hemisphere. Then, hemisphere is fully filled
with sand or salt. It means that hemisphere contains double of the amount of sand/salt as contained by cone.
6. Let the cone be filled with sand or salt and pour it thrice into the cylinder. Then, cylinder is fully filled with
sand or salt. It means that cylinder contains triple of the amount of sand/salt as contained by cone.

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