Question
The radius of a cone is 7 cm, and its height is 24 cm. A
sphere is inscribed in the cone, touching the base and the curved surface. Find the radius of the sphere.Solution
For an inscribed sphere in a cone, the radius of the sphere r is given by the formula: r = (r × h) / √(r² + h²), where r is the radius of the cone’s base, and h is its height. Substituting the values: r = (7 × 24) / √(7² + 24²) = 168 / √(49 + 576) = 168 / 25 = 6.72 cm.
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