Question

A 40-lb container of peat moss measures 14x20x30 in. A 40-lb container of topsoil has a volume of 1.9 gal. (a) Calculate the average densities of peat mass and topsoil in units of g/cm3. Would it be correct to say that peat moss is "lighter" than topsoil? Explain. (b) How many bags of the peat moss are needed to cover an area measuring 10 ft. by 20 ft. to a depth of 20 in.?

Answer 1

@robtobey please help me with this problem.

Answer 2

@kelliegirl33 please help me with this problem. :33

Answer 3

Hi! Do you know the concept of density?

Answer 4

measure of compactness of matter

Answer 5

Pretty much! And for math, it's mass per volume.

Answer 6

Yeah. That's right

Answer 7

Lower density is the "lighter" that the problem mentioned.

Answer 8

And it wants to know if peat moss is less dense than topsoil. So let's find the density of each!

Answer 9

Yeah, and my answer in letter a is 0.1. I'm not pretty sure about my answer.

Answer 10

It wants three answers there, actually.

1. Density of peat moss.
2. Density of top soil.
3. If peat moss is less dense than top soil.

Answer 11

Pounds is a measure of force. It's actually the weight, here. But we'll want it in metric - newtons.\[1\ [lb]=4.44822162\ [N]\]\[40\ [lb]=177.9[N]\]
And \[F_{weight}=mg\qquad\implies\qquad m=\frac{F_{weight}}{g}\]

Answer 12

So you can get the mass that makes a weight of \(40\ [lb]\). That will help for both peat moss and top soil.

Answer 13

Does that make sense so far?

Answer 14

Yeah.

Answer 15

The mass will be in kilograms, though. You'll have to multiply by 1000 to get the number of grams.

How good are you at converting?

Answer 16

I'm done converting it. 1.8 x10^4g

Answer 17

that's the conversion

Answer 18

You have the volume as "14x20x30 in", and the product will be the volume in cubic inches. But you'll have to convert that to cubic centimeters. You'll have to do the same with the gallons.

And remember what density is.\[\rho=\frac{m}{V}\]

So, when you need the number of bags for part b, you'll need the number of pounds necessary for that volume. You'll know \(\rho\) and \(V\), and you'll solve for \(m\).

Then, you'll use the \(m\) to find \(m\ g\). Then you'll get it into units of pounds. You'll have to divide that by \(\Large \frac{40\ [lb]}{1\ [bag]}\) to find how many bags you'll need. Of course, you'll need to round up, so you make sure you have enough bags for that volume.

Answer 19

That's what I got for the grams, too!

Answer 20

I'll be back. Let's continue this after i finish eating :)

Answer 21

I have to go! If I'm not on later, good luck! I hope those instructions help.

Google will help with conversion amounts, and I bet there are other sites as well.