1. ## [SOLVED] Cylinders

Hi, I am trying to help my daughter with her homework. She finished the last 20 question by herself and has 2 left that she's been stuck on for over an hour. Can anyone here lend a hand? She's giving it all she's got, just stuck.

1. What is the volume of a cylinder with a 4" diameter and 5" stroke?

2. A cylinder of gas 6'' tall contains 10 psi with 300cu. Inches of volume. If this is compressed down to 2" tall, what will be the pressure and volume if temp is held constant?

Thanks a Bunch!

2. Originally Posted by mimiyumichan

2. A cylinder of gas 6'' tall contains 10 psi with 300cu. Inches of volume. If this is compressed down to 2" tall, what will be the pressure and volume if temp is held constant?
ok, i don't know what the stroke of a cylinder is (should i be embarrassed about that?), so i can't help you with the first, but for the second, this is the way to go.

For a cylinder, the volume, V, is given by:

$V = \pi r^2 h$
where $r$ is the radius of the base of the cylinder, and $h$ is height of the cylinder.

when the height is 6, the volume is 300

$\Rightarrow V = 300 = \pi r^2 (6)$ .......divide both sides by 6

$\Rightarrow \pi r^2 = 50$

So, when the height goes to 2, the volume will be:

$V = \pi r^2 (2) = 50 \cdot 2 = 100 in^3$

Now by Boyles' Law:

$P_{1} V_{1} = P_{2} V_{2}$

$\Rightarrow P_{2} = \frac {P_{1} V_{1}}{V_{2}}$

$\Rightarrow P_{2} = \frac {10 \cdot 300}{100}$

$\Rightarrow P_{2} = 30 psi$

So the new volume is 100 cubic inches and the new pressure is 30 psi