The diameter-to-height ratio of a right circular cone is

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