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algebra, mathematics

"The diagram shows a solid cylinder. The cylinder has a radius of 2y and height of 6y.
The cylinder is melted down and made into a sphere of radius r.
Express r in terms of y."

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  1. this is due tmrw and im on the verge of a breakdown 💀

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  2. volume of cylinder:

    Area of circle • height =

    ( 2 y)^2π • 6 y = 4 y^2 π • 6 y =

    24 y^3 π

    When the cylinder is melted down volume of material is same.

    volume of sphere:

    4 / 3 r^3 π

    24 y^3 π = 4 / 3 r^3 π

    Divide both dides by 4 π

    6 y^3 = r^3 / 3

    Multiply both sided by 3

    18 y^3 = r^3

    r^3 = 18 y^3

    r = ∛18 y

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  3. for a cylinder,
    v = πr^2 h = π(2y)^2 * 6y = 24πy^3
    for a sphere,
    v = 4/3 πr^3 = 24πy^3
    so r^3 = 3/(4π) * 24πy^3 = 18
    r = ∛18

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  4. go with Bosnian. My typo didn't include the y.

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  5. tysm!! i got 100% :))

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