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Algebra

This diagram shows a solid metal cylinder.

The cylinder hasbase radius 2x and height 9x.
The cylinder is melted down and made into a sphere of radius r
Find an expression for in terms of x

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  1. Volume of cylinder = ( 2 x ) ² ∙ π ∙ 9 x = 4 x² ∙ π ∙ 9 x = 36 x³ ∙ π

    Volume of a sphere with radius r = ( 4 / 3 ) ∙ π ∙ r³

    Volume of cylinder = Volume of a sphere

    36 x³ ∙ π = ( 4 / 3 ) ∙ π ∙ r³

    Divide both sides by π

    36 x³ = ( 4 / 3 ) ∙ r³

    Multiply both sides by 3

    36 x³ ∙ 3 = 4 ∙ r³

    108 x³ = 4 ∙ r³

    Divide both sides by 4

    27 x³ = r³

    r³ = 27 x³

    r = ∛ (27 x³ )

    r = 3 x

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