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Question
"Area A oof a circular ring formed by 2 concentric circles is equal to the product of pie and the difference of the square of the bigger radius R and the square of the bigger radius R and the square of the smaller radius r. Express the above statement as a formula. Make r the subject of the formula and find r, when A = 88 sq cm and R = 8cm.
Solution
Radius of bigger circle = R
Radius of smaller circle = r
Area = A = π(R2 - r2)
⇒ A = π(R2 - r2)
⇒ `"A"/pi = "R"^2 - "r"^2`
⇒ r2 = `"R"^2 - "A"/pi`
⇒ r = `sqrt("R"^2 - "A"/pi)`
Putting A = 88cm2 and R = 8cm
⇒ r = `sqrt(8^2 - 88/(22/7)`
= 6cm.
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