Question

Please show me all the solutions to these problems.

6. Convert 500 CFM (cubic feet per minute) to gallons per day.

7. An eight-ounce cup of Starbuck’s cappuccino has 75 mg of caffeine. How many
grams of caffeine are in 3 gallons of cappuccino? There are two cups in a pint, two
pints in a quart and 4 quarts in a gallon.

8. Express 150 ng in μg.

9. Express 81 mg in μg.

10. Express 13 μm in nm.

Answer 1

6. Solution:

1 Cubic feet (CF) = 7.48 gallons

500 CF = 7.48*500 = 3740 gallons

So, 500 CFM (cubic feet per minute) = 3740 gallons per minute

As there are 60 minutes in one hour,

3740*60 = 224400 gallons per hour

As there are 24 hours in one day,

224400*24 = 5385600 gallons per day

So, 500 CFM is equal to 5385600 gallons per day.

7. Solution:

Given that an eight-ounce cup of cappuccino has 75mg of caffeine.

75 mg = 75*10^–3 = 0.075g

1 fluid ounce = 0.0078 gallons

8 ounces = 0.0078*8 = 0.0624 gallons.

So, 0.0624 gallons of cappuccino has 75mg or 0.075g of caffeine.

If 0.0624 gallons of cappuccino has 75*10^–3g of caffeine, then 1 gallon of cappuccino has (0.075)/0.0624 = 1.2g of caffeine.

Then, 3 gallons of cappuccino will have 1.2*3 = 3.6g of caffeine.

8. Solution:

1ng = 1*10^–3μg = 0.001μg

Therefore, 150ng = 150*0.001 = 0.150μg

So, 150ng = 0.150μg = 150*10^–3μg​​​​​​​

9. Solution:

1mg = 1000μg =1*10³μg

So, 81mg = 81*1000 = 81000μg

So, 81mg = 81000μg

10. Solution:

1μm = 1000nm = 1*10³nm

13μm = 13*1000 = 13000nm

So, 13μm = 13000nm