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# The Sum of the Radii of Two Circles is 140 Cm and the Difference of Their Circumferences in 88 Cm. Find the Diameters of the Circles. - CBSE Class 10 - Mathematics

ConceptPerimeter and Area of a Circle

#### Question

The sum of the radii of two circles is 140 cm and the difference of their circumferences in 88 cm. Find the diameters of the circles.

#### Solution

Let radius of circles be 𝑟1𝑎𝑛𝑑 𝑟2

Given sum of radius = 140cm

𝑟1 + 𝑟2 = 140 …..(i)

difference in circumferences = 88 𝑐𝑚

2 × 𝑟1 − 2𝜋𝑟2 = 88

2 × 22/7 (r_1 − r_2) 88

r_1-r_2 = (88xx7)/(2xx22) = 14

r_1 = r_2 +14….(ii)

(𝑖𝑖)𝑖𝑛 (𝑖) ⇒ r_1 + r_2 +14 =140

⇒ 2𝑟2 = 126

⇒ 𝑟2 = 126/2 = 63𝑐𝑚𝑠

𝑟2 = 63𝑐𝑚𝑠 𝑖𝑛 (𝑖𝑖) 𝑟1 = 63 + 14 = 77 𝑐𝑚𝑠

Diameter of circle (i) = 2𝑟1 = 2 × 77 = 154 𝑐𝑚𝑠

Diameter of circle (ii) = 2𝑟2 = 2 × 63 = 126 𝑐𝑚𝑠

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Solution The Sum of the Radii of Two Circles is 140 Cm and the Difference of Their Circumferences in 88 Cm. Find the Diameters of the Circles. Concept: Perimeter and Area of a Circle.
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