Subject: science-density and volume
Name: Patricia
Who are you: Student (Middle)

Dear Stephen and Harley,
Thanks you so much for promptly answering my questions. You have been a great help.

I have 2 questions for you this time. I hope you will not get tired of helping me. I really appreciate it.

1. Nick has to ship 650,000 g of substance A to Singapore. The density of substance A is 3.23g/cm3. If the delivery charge is 0.25 centavo per cm3,how much does he need to pay?

2.Ann ordered 150 balloons for a birthday. Each balloon has a radius of 20cm. If the density of helium is 0.124g/cm3,how many grams of helium is needed to meet the order?

Thank you.

 


Hi.

I'll show you how to analyze this kind of problem so you can do this
on your own.

You have a mass quantity, a density, cost per unit volume and you want the total cost. The best way to tackle these problems is to analyze the units (dimensions) involved.

Look at the dimensions and work backwards:

  1. You want the total cost C, but cost is only expressed in terms of volume because of the rate R in cost per unit volume V. So C = RV. You know R but you need V now.

  2. To get V, you have density D (mass M per unit volume V) so V = M/(M/V) = M/D. You know both M and D.

So you can put these together: C = RV, V = M/D. That means C = RM/D.

Now let's double-check with the units themselves:

RM/D = (centavos / cm3) (g) / (g / cm3) = centavos because the others cancel.

That confirms our units. So now all that is left is to replace the variables R, M, and D with the actual numbers in the question and calculate C.

Stephen La Rocque>