Question 284014
i have to find the radius of a hollow sphere
The metal in the sphere is 3cm thick and the volume of the metal is 684 times pi cm cubed.
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Volume of a sphere = {{{4*pi*r^3/3}}}
The volume of the 3 cm wall is the volume of a sphere of radius (r+3) minus a sphere or radius r.
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{{{684*pi = (4*pi/3)*((r+3)^3 - r^3)}}}
{{{684 = (4/3)*(r^3 + 9r^2 + 27r + 27 - r^3)}}}
{{{171 = (1/3)*(9r^2 + 27r + 27)}}}
{{{171 = 3r^2 + 9r + 9}}}
{{{57 = r^2 + 3r + 3}}}
{{{r^2 + 3r - 54 = 0}}}
(r + 9)*(r - 6) = 0
r = 6 cm (inside radius)
r = 9 cm (outside radius)