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Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere?

Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere? Correct Answer 5 : 3

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Radius of base of cone = BD = 8 cm and Height CD = 15 cm

∴ CB2 = 64 + 225 = 289

⇒ CB = 17 cm

We can say that the sphere inside the cone will act as the in circle of ΔABC;

∴ In radius = R = ∆/s

∆ = 1/2 × 15 × 16 = 120

s = (17 + 16 + 17)/2 = 25

∴ In radius = R = 120/25 = 24/5

∴ Ratio of radius of base of cone to the radius of sphere = 8 : (24/5) = 5 : 3

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