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A solid sphere of radius 13 cm is melted and its some part is used to cast a hollow sphere whose internal radius is 5 cm. What will be the thickness of the sphere if the surface area of solid sphere is equal to the total surface area of hollow sphere?

A solid sphere of radius 13 cm is melted and its some part is used to cast a hollow sphere whose internal radius is 5 cm. What will be the thickness of the sphere if the surface area of solid sphere is equal to the total surface area of hollow sphere? Correct Answer 7 cm

Given:

Radius of sphere = 13 cm

Surface area of solid sphere is equal to the total surface area of hollow sphere

Formula used:

Surface area of sphere = 4 × π × (radius)2

Calculation:

Internal radius of the sphere = 5 cm

Let the thickness of the sphere be x cm

External radius of the sphere = (5 + x) cm

Surface area of the solid sphere = Total surface area of the hollow sphere

4 × π × (13)2 = 4 × π ×

⇒169 = (25 + 25 + x2 + 10x)

⇒ x2 + 10x = 119

⇒ x = 7 cm

Hence, the thickness of the hollow sphere = x = 7 cm

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