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Answer:
Answer:
The radius of the inner circle is 14cm.
Step-by-step explanation:
Let the radius of the inner circle = r
Given :
Area enclosed between two concentric circles, A = 770 cm ^ 2
Radius of the outer circle, R = 21cm
Area enclosed between two concentric circles, A = Area of the Outer circle - Area of the inner circle
770 = Pi * R ^ 2 - Pi * r ^ 2
77O = Pi(R ^ 2 - r ^ 2)
770 = Pi(21 ^ 2 - r ^ 2)
770 = Pi(441 - r ^ 2)
770 = 22/7 * (441 - r ^ 2)
770 * 7 = 22(441 - r ^ 2)
(441 - r ^ 2) = 770 * 7 / 22
(441 - r ^ 2) = (70 * 7) / 2
(441 - r ^ 2) = 35 * 7
245 = 441 - r ^ 2
r ^ 2 = 441 - 245
r ^ 2 = 196
r = √196
r = 14
r = 14cm
Hence, the radius of the inner circl is 14cm.
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Verified answer
Answer:
r = 14 cm
Step-by-step explanation:
Radius of outer circle (R) = 21 cm
Let the radius of inner circle be = r cm
Area enclosed between concentric circle = 770²
[tex]\pi \: R² \: - \pi \: {r}^{2} = 770 \\ \frac{22}{7} \times 21 \times 21 \ \times {r}^{2} = 770 \\ \frac{22}{7} (441 - r {}^{2} ) = 770 \\ 441 - {r}^{2} = \frac{770 \times 7}{2} \\ 441 - {r}^{2} = 245 \\ {r}^{2} = 441 - 245 \\ {r }^{2} = 196 \\ r = \sqrt{196} = 14 \\ 14cm[/tex]
Therefore, the radius of inner circle is = 14 cm.
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