Question

An electronics company used a pipe that was 100 ft long and had a radius of 10 ft. Inside the pipe was a smaller cylindrical tube, for wires, that had a radius of 2 ft and was as long as the pipe. The remaining space in the pipe, outside the tube, was filled with liquid foam.

What was the volume of the foam inside the pipe? Use 3.14 to approximate pi.

Answer 1

Would you be able to compute the volume if there wasn't a hole in the middle?

Answer 2

no

Answer 3

OK, I'm assuming then that you don't recall the formula for the volume of a cylinder?

\[V_{cyl} = \pi r^2 h\]
r is the radius of the cylinder, and h is the height of the cylinder.

Answer 4

Notice that this formula just calculates the area of the circle on the bottom (pi r^2) and then stacks them up to a height of h (h times pi r^2).

Answer 5

So, now, ignoring the hole in the middle for the moment, what would the volume be given r = 10 ft, and h = 100 ft ?

Answer 6

110?

Answer 7

Looks like you added the two together... Did you use the formula that I provided? Or maybe you have a question on how to use the formula? :)

Answer 8

It's a little weird when you first use it, so let me show you how to compute this one:

r = 10
h = 100

V = pi*r^2 * h

V = pi*(10)^2 * 100
V = pi*100*100
V = 10000*pi = 31400

Does that make sense?

Answer 9

no

Answer 10

Alright, do you understand why r = 10 and h = 100 if we ignore the hole for now?

Answer 11

yes

Answer 12

@jtvatsim

Answer 13

OK, are you willing to accept that V = pi*r^2 * h is the definition of volume for a cylinder?

Answer 14

yeah

Answer 15

OK, so, where did you get lost in the process to get 31400 as the volume without a hole? I just plugged in the numbers and solved... we still have another step to do to get the "final" answer... if that was your question?

Answer 16

I assumed that pi = 3.14 as an approximation, if you wondered how that happened :)

Answer 17

i thought you were going to explain how to do it

Answer 18

How to do the "whole" problem? I am, I just was checking to make sure you understand up to this point.

Answer 19

yes

Answer 20

Oh, OK, miscommunication there. :)

Answer 21

Alright, so now that's great that we have the volume without the hole (31400), but that doesn't give us the actual answer we want. To do that, we will need to find out the volume of the hole and subtract that from the volume we found first.

Answer 22

Basically, Volume of the foam = Volume without hole - Volume of the hole.

Answer 23

So, what is the volume of the hole? This time we have r = 2, and h = 100 (that's the radius of the hole). Good so far?

Answer 24

Have a try at it... plug in r = 2 and h = 100, use pi = 3.14, into the equation V = pi*r^2 * h and tell me what you get. :)

Answer 25

am i supposed to multiply?

Answer 26

@jtvatsim

Answer 27

Yes pi (multiplied by) r^2 (multiplied by ) h

Be sure to remember that r^2 means r (multiplied by) r.

Answer 28

628

Answer 29

Very close! You might have missed a 2 when you were multiplying:

You should have: 3.14 x 2 x 2 x 100.

Answer 30

That's because we have r^2 = r x r. So, we have to do 2^2 = 2 x 2 after plugging in r = 2. Does that make sense? The answer should be 1256.

Answer 31

yeah

Answer 32

what's next

Answer 33

Alright, so we know that the volume without a hole is 31400 and the volume of the hole itself is 1256. So the actual volume is just subtraction 31400 - 1256 = 30144 and of course the units are cubic feet.

Answer 34

I hope that helps... phew, that was a long one (but our misunderstanding earlier didn't help). :) Any questions?

Answer 35

is that it

Answer 36

@jtvatsim