Page 245 - Start Up Mathematics_7

Step 3: Measure the circumference of each circular object by encircling a fine thread around
it. Straighten the thread and measure it.
Record your measurements in the following table.

Ratio of Circumference and
Diameter of the Circumference of  C 
Circle No. Diameter  
Circle (d = 2r) the Circle (C)  2r 

Observation: In each case you will observe that the ratio of circumference and diameter is
constant and is approximately equal to 3.14. This ratio is denoted by the symbol ‘π’ (pi).
22
Thus, π = 3.14 = (approximately)
7
Circumference C
Thus, = π ⇒ C = = π ⇒ C = 2πr
Diameter 2r

Area of a Circle

Area of a circle of radius r = πr 2 (where approximate value of π is 22 )
7
Example 17: Find the circumference of the circles whose radius is: (Take π = 22 )
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(a) 35 cm (b) 21 mm
22
Solution: (a) Circumference = 2πr = 2 × 7 × 35 = 220 cm

22
(b) Circumference = 2πr = 2 × × 21 = 132 mm
7 22
Example 18: Find the area of the following circles: (Take π = 7 )
(a) radius = 7 mm (b) diameter = 12 cm
22
2
Solution: (a) Area of the circle = πr = 7 × 7 × 7 = 154 mm 2
Diameter 12
(b) Radius (r) = = = 6 cm
2 2
2
∴ area of the circle = πr = 22 × 6 × 6 = 792 = 113.14 cm 2
7 7
Example 19: If the circumference of a circular sheet is 132 cm, find its radius and area.
(Take π = 22 )
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Solution: Circumference of the circular sheet = 132 cm
22
∴ 2 × × r = 132 cm (Circumference = 2πr)
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⇒ r = 132 × 7 = 21 cm
2 × 22
22
2
Area of the circular sheet = πr = × 21 × 21 = 1,386 cm 2
7
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