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.

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.

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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

Related Questions

Find the area of a triangle whose perimeter is 22 cm, one side is 9 cm and the difference of other two sides is 3 cm.

The base of an isosceles triangle is 24 cm and its area is 60 cm². Find its perimeter.

Water flows into a tank, 150 metres long and 100 metres broad, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep ?

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

Related Questions

Find the area of a triangle whose perimeter is 22 cm, one side is 9 cm and the difference of other two sides is 3 cm.

The base of an isosceles triangle is 24 cm and its area is 60 cm2. Find its perimeter.

Water flows into a tank, 150 metres long and 100 metres broad, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep ?

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.

The base of an isosceles triangle is 24 cm and its area is 60 cm². Find its perimeter.