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प्रश्न
Find the area enclosed between two concentric cirdes of radii 6.3 cm and 8.4 cm. A third concentric circle is drawn outside the 8.4 cm circle, so that the area enclosed between it and 8.4 cm cirde is the same as that between two inner circles. Find the radii of the third circle correct to two decimal places .
उत्तर
Radius of innermost circle = r1 = 6.3 cm
Radius of central circle= r2 = 8.4 cm
Area between two inner circles = π r22 - π r12
`= π (8.4)^2 - pi (6.3)^2`
= 70.56 π - 39.69 π .........(i)
= 221.76 - 124.74
= 97.02 cm2
Area between two inner circles = 97.02 cm2
Let radius of third circle be r
Area between next two circles = `pi "r"^2 - pi "r" 2^2`
`= pi "r"^2 - pi (8.4)^2`
`= pi "r"^2 - 70.56 pi` .........(ii)
Given that (i) and (ii) are equal
⇒ πr2 - 70.56 π = 70.56 π - 39.69 π
⇒ r2 - 70.56 = 70.56 - 39.69
⇒ r2 = 70.56 - 39.69 + 70.56
⇒ r2 = 101.43
⇒ r = 10.07 cm
Therefore, radius of third circle is 10.07 cm
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