Deepak Bora
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Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere

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Problem was asked in 2012 cbse board exam. Problem from RS Aggarwal book problem number 3, exercise 17B, chapter volume and surface area of solid, page number 809

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  1. The radii r1 = 6 cm,

    r2 = 8 cm

    r3 = 10 cm

    Let the radius of the resulting sphere be R.

    Volume of resulting sphere = Volume of three metallic spheres
    [4/3]πR³ =([4/3]πr1³) + ([4/3]πr2³) + ([4/3]πr3³)

    [4/3]πR³ =([4/3]π*6³) + ([4/3]π*8³) + ([4/3]π*10³)

    [4/3]πR³ = [4/3]π ( 6³ + 8³ + 10³ )

    R³ = 216 + 512 + 1000

    R³ = 1728

    ∴ The radius of the resulting sphere is 12 cm

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