Question

A cylinder with radius r and height 2r +4 contains a cube with edge length r times square root of 2. What fraction of the cylinder's volume is taken up by the cube. Write in simplified form.

Answer 1

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)

Answer 2

thank you!!! You're the best!

Answer 3

Np,
No you are :D.

Answer 4

Glad i could help :)!