Question
The combined height and radius of a right circular cone
total 31 cm, with the height exceeding the radius by 17 cm. Calculate the curved surface area of the cone.Solution
Let the radius and height of the cone be 'r' cm and 'h' cm respectively. We have, (r + h) = 31 And h = r + 17 So, r + h = r + r + 17 = 31 Or, r = (31 - 17) ÷ 2 = 7 cm So, h = 7 + 17 = 24 cm Also, slant height of the cone = √(r2 + h2) = √(7 2 + 24 2) = 25 cm Therefore, curved surface area of the cone = π X radius X slant height = (22/7) X 7 X 25 = 550 cm2
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