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In Figure 6, Three Circles Each of Radius 3.5 Cm Are Drawn in Such a Way that Each of Them Touches the Other Two. Find the Area Enclosed Between These Three Circles (Shaded Region). [ U S E π = 22 7 ] - Mathematics

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ConceptCircles Examples and Solutions

Question

In Figure 6, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). `[Use pi=22/7]`

Solution

The given information can be diagrammatically represented as follows: 

Here, A, B and C are the centres of the circles. 

Radius of each circle, r = 3.5 cm 

Thus, the measure of each of the sides of ΔABC is 3.5 cm + 3.5 cm = 7 cm. 

Since the sides of triangle ABC are of equal lengths, it is an equilateral triangle. 

∴ ∠A = ∠B = ∠C = 60° 

Area of the shaded region = Area of ΔABC − (sum of areas of sectors APR, BPQ and CQR) 

`=sqrt3/4a^2-3xxO//360^@xxpir`

`=1.732/2xx(7cm)^2-3xx60^@/360^@xx22/7xx3.5cmxx3.5cm`

`=21.217 cm^2-19.25cm^2`

`=1.97cm^2`

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Solution In Figure 6, Three Circles Each of Radius 3.5 Cm Are Drawn in Such a Way that Each of Them Touches the Other Two. Find the Area Enclosed Between These Three Circles (Shaded Region). [ U S E π = 22 7 ] Concept: Circles Examples and Solutions.
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