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Radius of base of a hollow cone is 5 cm and its height is 12 cm. What is the approximate surface area of the largest sphere that can be put inside this cone?

Radius of base of a hollow cone is 5 cm and its height is 12 cm. What is the approximate surface area of the largest sphere that can be put inside this cone? Correct Answer 140 cm<sup>2</sup>

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Radius of the cone = 5 cm and Height = 12 cm.

PR = √(25 + 144) = 13 cm

We can observe that the sphere inside the cone will act as the incircle of ΔPQR.

PQ = PR = 13 cm, QR = 10 cm, PS = 12 cm

∴ s = (13 + 13 + 10)/2 = 18 cm

Area of the triangle = 1/2 × 12 × 10 = 60 cm2

∴ Inradius = (Area)/s = 60/18 = 10/3 cm

∴ Radius of the sphere = 10/3 cm

∴ Surface area of the sphere = 4 × 22/7 × 10/3 × 10/3

⇒ 8800/63 = 139.68 ≈ 140 cm2

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