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Circles

Concepts Explained Through Illustrations

Circumference = 2R. Where R = Radius of the circle, which is half of the diameter.

Circumference is the outer boundary of the circle.

Area = R2.    

 

Illustration 1 :

The diameter of a circle is 14 cm. Find its area and circumference.

Solution

Diameter = 14 cm, Radius ⇒ Half of diameter ⇒ 14/2 = 7 cm
Area = R2 = (22/7) × 7 × 7  ⇒ 154 sq. cm.

Circumference = 2R = 2 × 22/7 × 7 = 44 cm


 

Illustration 2 :

The circumference of a cricket is 88 cm. Find its area.

Solution

Circumference = 2R ⇒ 88 = 2 × 22/7 × R ⇒ 88 × 7/22 × ½ = 14 cm
Area = R2 = 22/7 × 14 × 14 = 616 sq. cm.

 
 

Sometimes the questions related to the number of revolutions a wheel will take to cover a certain distance, are asked. In that case the number of revolutions = Distance ÷ 2R.  In one revolution the distance covered by the circle is equal to the circumference.

 

 

Illustration 3 :

The diameter of a circle is 21 metres. How many revolutions will it take to cover a distance of 6.6 km?

Solution

In this case, the total distance is given in terms of km. First, convert in metres by multiplying it 1000. Distance = 1000 × 6.6 = 6600 meters.
No. of revolutions = 6600/2 × 22/7 × 21/2 = 100 revolutions.

 





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