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The curved surface area of a right circular cone is 12320 cm². If the radius of its base is 56cm, then find its height.

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Question 4 The curved surface area of a right circular cone is 12320 cm². If the radius of its base is 56cm, then find its height. Let Radius of cone = r = 56 cm Height of cone = h Slant height of cone = l Given that Curved Surface Area of cone = 12320 πrl = 12320 22/7× 56 × 𝑙= 12320 22 × 8 × 𝑙= 12320 𝑙 = (12320/(22 × 8)) cm 𝒍 = 70 cm Finding Height We know that l2 = h2 + r2 (70)2 = h2 + (56)"2" 702 − 562 = h2 h2 = 702 − 562 h2 = (70 − 56)(70 + 56) h2 = 14 × 126 h2 = (7 × 2) × (63 × 2) h2 = (7 × 2) × (7 × 9 × 2) h2 = (7 × 7) × (2 × 2) × 9 h2 = 72 × 22 × 32 h2 = (7 × 2 × 3)2 h2 = 422 h = 42 cm Therefore, the height of the cone is 42 cm.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.