Question
The diameter-to-height ratio of a right circular cone is
16:15. Given that the curved surface area is 1224 π cm2, determine the cone's slant height.Solution
Let the diameter and height of the given cone be '16x' cm and '15x' cm respectively. So, radius = 16x ÷ 2 = '8x' cm Let the slant height of the cone be 's' cm We know, slant height2 = radius2 + height2 So, s2 = (8x) 2 + (15x) 2 Or, s = √(64x2 + 225x2) Or, s = √289x2 So, 's' = '17x' Curved surface area of cone = π X radius X slant height 1224π = π X 8x X 17x Or, 1224 = 136x2 Or, 9 = x2 So, 'x' = ±3 Since, 'x' cannot be negative, Therefore, slant height of the cone = '17x' = 17 x 3 = 51 cm
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