Mathematics Lab Activity-16 Class IX | Surface Area & Volume

 Lab Activity-16 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 - 16

Objective: 

To obtain the formula for the surface area of a sphere.

Material Required:

A ball, cardboard/wooden strips, thick sheet of paper, ruler, cutter, string, measuring tape, adhesive.

Procedure:

1. Take a spherical ball and find its diameter by placing it between two vertical boards (or wooden strips) [see Fig. 1]. Denote the diameter as d.

Figure 1

2. Mark the topmost part of ball and fix a pin [see Fig. 2].

Figure-2

3. Taking support of pin, wrap the ball (spirally) with string completely, so that on the ball no space is left uncovered [see Fig. 2].
4. Mark the starting and finishing points on the string, measure the length between these two marks and denote it by l. Slowly, unwind the string from the surface of ball.
5. On the thick sheet of paper, draw 4 circles of radius ‘r’ (radius equal to the radius of ball).
6. Start filling the circles [see Fig. 3] one by one with string that you have wound around the ball.

Figure 3

7. Let the length of string which covers a circle (radius r) be denoted by a.

8. The string which had completely covered the surface area of ball has been used completely to fill the region of four circles (all of the same radius as of ball or sphere).

9. This suggests:

Length of string needed to cover sphere of radius r = 4 × length of string needed to cover one circle i.e., l = 4a

or, surface area of sphere = 4 × area of a circle of radius r

So, surface area of a sphere = 4πr².

Observations

Diameter d of the spherical ball =14 cm.

Radius r =7 cm.

Length l of string used to cover ball = 480 cm.

Length a of string used to cover one circle =120 cm.

So length of the string (l) = 4 × 120 cm = 480 cm

Surface area of a sphere of radius r = 4 × Area of a circle of radius r = 4πr².

Result : 

Surface area of sphere = 4πr².

Applications

This result is useful in finding the cost of painting, repairing, constructing spherical and hemispherical objects.

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