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.

Answer 1

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.