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In the figure (i) given below, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

In the figure, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Mensuration

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Answer

Radius of circle with center A = AC = 8 cm.

Area of circle with center A = πr2

= 227×82=22×647\dfrac{22}{7} \times 8^2 = \dfrac{22 \times 64}{7}

= 14087\dfrac{1408}{7} = 201.14 cm2.

From figure,

BC = AC - AB = 8 - 3 = 5 cm.

Area of circle with center B = πr2

= 227×52=22×257\dfrac{22}{7} \times 5^2 = \dfrac{22 \times 25}{7}

= 5507\dfrac{550}{7} = 78.57 cm2.

Area of shaded region = Area of circle with center A - Area of circle with center B

= 201.14 - 78.57

= 122.57 cm2.

Hence, area of shaded region = 122.57 cm2.

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