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27 April, 11:03

A sphere and a cylinder have the same radius and height. The volume of the cylinder have the same height and radius. The volume of the cylinder is 27pi ft. What equation gives the volume of the sphere?

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  1. 27 April, 11:16
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    Step-by-step explanation:

    radius of sphere, rs

    radius of cylinder, rc

    height of cylinder, h

    given: h = rs = rc = r ... eq1

    volume of cylinder, vc = 27pi ft ... eq2

    volume of cylinder, vc = pi * rc^2 * h ... eq3

    volume of sphere, vs = 4/3 (pi*rs^3) ... eq4

    subst for h & rs from eqn 1 in eqn 3 ...

    vc = pi x r^2 x r = pi x r^3 ... eqn 5

    subst for vc from eqn 2 in eqn 5 ...

    => 27 pi ft = pi x r^3

    => 27 = r^3

    => r = 3ft ... eqn 6

    subst for rs from eqn 1 in eqn 4

    vs = 4/3 (pi x r^3) ... eqn7

    subst for pi x r^3 from eqn 5 in eqn 7

    vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft
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