# 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 = R^{2}. ** **

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

Diameter = 14 cm, Radius â‡’ Half of diameter â‡’ 14/2 = 7 cm

Area = R^{2} = (22/7) Ã— 7 Ã— 7 â‡’ 154 sq. cm.

# Circumference = 2R = 2 Ã— 22/7 Ã— 7 = 44 cm

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

Circumference = 2R â‡’ 88 = 2 Ã— 22/7 Ã— R â‡’ 88 Ã— 7/22 Ã— Â½ = 14 cm

Area = R^{2} = 22/7 Ã— 14 Ã— 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 Ã· 2R. In one revolution the distance covered by the circle is equal to the circumference.

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

In this case, the total distance is given in terms of km. First, convert in metres by multiplying it 1000. Distance = 1000 Ã— 6.6 = 6600 meters.

No. of revolutions = 6600/2 Ã— 22/7 Ã— 21/2 = 100 revolutions.