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    Question

    The ratio of volumes of spheres A and B is 8:27. If the

    difference between their total surface area is 3080 cm┬▓ then find diameter of sphere A. (in cm)
    A 10 cm Correct Answer Incorrect Answer
    B 28 cm Correct Answer Incorrect Answer
    C 12 cm Correct Answer Incorrect Answer
    D 24 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Volume ratio A:B = 8:27 тЖТ radii ratio = 2x : 3x Surface area of A = 4╧А(2x)┬▓ = 16╧Аx┬▓ Surface area of B = 4╧А(3x)┬▓ = 36╧Аx┬▓ Difference = 36╧Аx┬▓ тАУ 16╧Аx┬▓ = 20╧Аx┬▓ = 3080 Solve: 20╧Аx┬▓ = 3080 x┬▓ = 3080 / (20 ├Ч 3.1416) тЙИ 49 x = 7 Radius of A = 2x = 14 Diameter = 2 ├Ч radius = 28 cm

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