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OpenStudy (jack1):
shoot
OpenStudy (anonymous):
A cylinder with radius r and height 2r+4 contains a cube with edge length r√2. What fraction of the cylinder’s volume is taken up by the cube? Write answer in simplified form.
OpenStudy (jack1):
so Volume of cube = S^3, yeah?
in this case = (r x sqrt 2)^3
OpenStudy (nathan917):
sqrt(2) r / Pi (r+2).
OpenStudy (anonymous):
right ok, but I am not sure what to do with it
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OpenStudy (jack1):
so volume of the cube =
\[2 \sqrt{2} r ^{3}\]
OpenStudy (anonymous):
right got that
OpenStudy (jack1):
Volume of cylinder = pi r^2 x ht
= (pi r^2) x (2r + 4)
OpenStudy (nathan917):
V_cylinder = (Pi r^2) (2r+4)
V_cube = (sqrt(2) r)^3 {I assume that's what you meant.}
Fraction = V_cyl / V_cube
= (2Pi r^3 + 4Pi r^2) / (2sqrt(2) r^3)
= (2Pi r + 4Pi) / 2sqrt(2) r = Pi (r+2) / sqrt(2) r
= Pi sqrt(2) (r+2) / 2r
Ed: Oops - I inverted this... the correct answer is sqrt(2) r / Pi (r+2)
OpenStudy (nathan917):
Ive answered this question b4.
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OpenStudy (jack1):
^^^^^^ what he said ;)
OpenStudy (nathan917):
:P.
OpenStudy (anonymous):
Thanks guys
OpenStudy (anonymous):
Nathan , you know I found that answer on the internet before right?