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14 July, 03:24

The ratio of the volumes of the two spheres is 27:343 and the sum of their radii is 10 units. Find the radius of the smaller sphere.

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  1. 14 July, 03:29
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    R + R = 10

    4/3 r³ π : 4/3 R³ π = 27 : 343

    r ³ : R ³ = 27 : 343 / ∛

    r : R = 3 : 7

    3 R = 7 r

    R = 7 r / 3

    r + 7 r / 3 = 10 / · 3

    3 r + 7 r = 30

    10 r = 30

    r = 30 : 10

    r = 3

    Answer: the radius of the smaller sphere is 3.
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