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    Question

    A solid metallic sphere of radius 15 cm is melted and

    recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all the balls?
    A 1:5 Correct Answer Incorrect Answer
    B 5:27 Correct Answer Incorrect Answer
    C 1:10 Correct Answer Incorrect Answer
    D 3:40 Correct Answer Incorrect Answer

    Solution

    Let the number of the smaller sphere be 'x' Volume of the bigger sphere = x × (volume of the smaller sphere) (4/3)π 15^3 = x × (4/3)π 3^3 x = 125 So their are total 125 smaller spheres Now, The surface area of the larger sphere = 4π 15 ⇒ 900π Surface area of smaller sphere = 4π 3^2 ⇒ 36π Total surface area of 125 smaller spheres = 125 × 36π ⇒ 4500π Surface area of the bigger sphere : Surface area of all smaller spheres = 900π : 4500π ⇒ 1 : 5

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