Question

A cylinder with radius r and height 2r + 4 contains a cube with edge length r√2, as shown. What fraction of the cylinder's volume is taken up by the cube? Write your answer in simplified form.

Answer 1

@SithsAndGiggles

Answer 2

Is there some kind of a diagram for this?

Answer 3

@staceyg

Answer 4

There's a model of the cylinder and cube.

Answer 5

@science0229

Answer 6

Sorry. Seems like we don't need a diagram for this one.
Do you know how to find the volume of a cylinder and a cube?

Answer 7

Volume of a cylinder=\[\pi r^2h\]
Volume of a cube=\[s^3\]

Answer 8

Cylinder=\[\pi r^2(2r+4)\]
Cube=\[(r \sqrt{2})^3=2\sqrt{2}r^3\]

Answer 9

fraction of the cylinder's volume is taken up by the cube=\[\frac{ cube }{ cylinder }=\frac{ \pi r^2(2r+4) }{ 2\sqrt{2}r^3 }=\frac{ \pi(r+2) }{ \sqrt{2}r }=\frac{ \pi \sqrt{2}(r+2) }{ 2r }\]

Answer 10

This is the simplest that you can get

Answer 11

Any questions?

Answer 12

@staceyg

Answer 13

No, thanks so much for explaining :)