The area of a circular ring enclosed between two concentric circles is 286 cm². Find the radii of the two circles, given that their difference is 7 cm.
Mensuration
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Question

The area of a circular ring enclosed between two concentric circles is 286 cm2. Find the radii of the two circles, given that their difference is 7 cm.

KnowledgeBoat · Accepted Answer

Given: The area of a circular ring = 286 cm2 The difference in radii of the two circles = 7 cm Let the radius of the larger circle = R cm Let the radius of the smaller circle = r cm Thus, we are given: R - r = 7 ...................(1) The area of the ring is given by the difference between the areas of the two circles: ⇒ πR2 - πr2 = 286 ⇒ π(R2 - r2) = 286 ⇒ (R2 - r2) = 286 ⇒ R2 - r2 = ⇒ (R - r)(R + r) = ⇒ (R - r)(R + r) = 91 ⇒ 7 x (R + r) = 91 ⇒ R + r = ⇒ R + r = 13 ...................(2) Adding both equations (1) and (2), we get: Substituting in equation (1), we get ⇒ 10 - r = 7 ⇒ 10 - 7 = r ⇒ r = 3 Hence, the radii of the two concentric circles are 10 cm and 3 cm.

Mathematics

The area of a circular ring enclosed between two concentric circles is 286 cm². Find the radii of the two circles, given that their difference is 7 cm.

Mensuration

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