Question

the area enclosed between two circles is 770cm². if the radii of the circles differ by 7cm, find both the radii​

Answer 1

Answer:

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Step-by-step explanation:

Let the radius of the inner circle = r

Given :

Area enclosed between two concentric circles , A = 770 cm²

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 = πR² – πr²

770 = π(R² - r²)

770 = π(21² – r²)

770 = π(441 - r²)

770 = 22/7 (441 - r²)

770 × 7 = 22(441 - r²)

(441 - r²) = 770 × 7 / 22

(441 - r²) = (70 × 7)/2

(441 - r²) = 35 × 7

245 = 441 – r²

r² = 441 – 245

r² = 196

r = √196

r = 14

r = 14cm  

Hence, the radius of the inner circle is 14cm.

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