Question
A cone has a base radius of 6 cm and a height of 8 cm. A
sphere is placed inside the cone such that it touches the base and the slant height of the cone. Find the radius of the sphere.Solution
The radius of the sphere can be found using the formula: Radius of sphere = (r × h) / (√(r² + h²) + r) Where r = 6 cm (radius of cone) and h = 8 cm (height of cone). Radius = (6 × 8) / (√(6² + 8²) + 6) = 48 / (√(36 + 64) + 6) = 48 / (√100 + 6) = 48 / (10 + 6) = 48 / 16 = 3 cm Correct Option: b
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