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The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

(A) 31 cm   (B) 25 cm   (C) 62 cm   (D) 50 cm

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Question 12 The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is (A) 31 cm (B) 25 cm (C) 62 cm (D) 50 cm Now, Area of 24 cm circle + Area of 7cm circle = Area of circle with radius r 𝜋(24)2 + 𝜋(7)2 = 𝜋r2 (24)2 + 72 = r2 Now, Area of 24 cm circle + Area of 7cm circle = Area of circle with radius r 𝜋(24)2 + 𝜋(7)2 = 𝜋r2 (24)2 + 72 = r2 576 + 49 = r2 625 = r2 r2 = 625 r2 = 252 r = 25 cm Thus, Diameter = 2 × 25 = 50 cm So, the correct answer is (D)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.