The difference in the areas of two concentric circles is 66 cm² and the radius of the outer circle is 11 cm. What is the radius of the inner circle?
(a) 8 cm
(b) 9 cm
(c) 10 cm
(d) 7 cm
Answers
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 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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Answer:
Radius = 10 cm
Step-by-step explanation:
area of outer circle = 11*11*22/7
= 121*22/7
=2662/7
=370 2/7 - 66 = 304 2/7
area of the inner circle = 10*10*22/7
=100*22/7
=2200/7
=304 2/7
radius of inner circle = 10 cm
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