A cylinder with radius and height 2r +4 contains a cube with edge length r When it's a good idea to start r√2. What fraction of the cylinders volume is taken up by the cube. Use a rational expression and write your answer in simplified form.

Question

anonymous · Answer

what does the second sentence mean? "When it's a good idea to start $$r*\sqrt{2}$$

anonymous · Answer

Sorry I messed the question up when I was trying to put in a square symbol. "When's it a good idea to start" shouldn't be in there.

anonymous · Answer

? So for this question can't you just calculate both volumes set up the ratio?

anonymous · Answer

I am not sure how to

anonymous · Answer

ok lets go through it. 

Volume of a cube is side^3, 
and this cube has side of length root(2)*r

anonymous · Answer

$$\left( \sqrt{2}*r \right)^3$$

anonymous · Answer

then the cylinder has a volume of length*base.

anonymous · Answer

height*

anonymous · Answer

so what is the area of the base?

anonymous · Answer

it would be the area of a circle with radius 2r+4

anonymous · Answer

can you calculate it?

anonymous · Answer

A = 2r +4 * 2r

anonymous · Answer

Oh I know whats confusing you. The problem writers were kind of mean when they used r as the variable, maybe it'll help if you consider the "r" an "x" in this case, because its not REALLY the radius.

anonymous · Answer

so the radius of the base is 2x+4
thus the area is 2pi(radius)^2

anonymous · Answer

so you're looking at 
$$2\pi*\left( 2x+4 \right)^2$$

anonymous · Answer

^^ that is the area of the base

anonymous · Answer

so if you have the base, then you multiply by the height to get volume.

anonymous · Answer

are you still with me?

anonymous · Answer

:( I hope you got it