Dimensional Analysis help!!!?

Question

I really do not understand dimensional analysis in chemistry. My teacher doesn't understand that nobody in the class understands it. i have homework due tomorrow and im going to get in trouble if i do not do it. Please do not think that i am lazy and just dont want to do it. if you want just tell me how to work out each problem and i will get the answer myself. any kind of help is appreciated. thanks.

1. A chemical plant process requires that a cylindrical reaction tank be filled with a certain liquid in 238 s. the tank is 1.2 m in diameter and 4.6 m high. what flow rate in liters per minute is required to fill the reaction tank in the specified time?

2.The radioactive decay of 2.8 g of plutonium-238 generates 1.0 joule of heat every second. Plutonium has a density of 19.86 g/cm^3. How many calories (1 cal=4.184 J) of heat will a ractangular piece of plutonium that is 1.5 cm x 3.05 cm x 15 cm generate per hour?

3. the mass of the earth is 5.974x10^24 kg. Assume that earth is a sphere of diameter 1.28x10^4 km and calculate the average density of earth in grams per cubic centimeter.

4.An automobile can travel 38 km on 4.0 L of gasoline if the automobile is driven 75% of the days in a year and the average distance traveled each day is 86 km, how many liters of gasoline will be consumed in one year (assume the year has 365 days)?

5. Automobile batteries are filled with a solution of sulfuric acid, which has a density of 1.285 g/cm^3. the solution used to fill the battery is 38% (by mass) sulfuric acid. How many grams of sulfuric acid are present in 500 mL of battery acid?

Answer 1

"dimensional analysis" here is just telling you that you need to pay close attention to the units in the problem.  I have read through all the questions here.  None of them is even slightly difficult.  If you do not know much chemistry, please consider them to be math problems.

1. The volume of the tank is:

3.14*(1.2/2)^2*4.6 = 5.2 m^3 = 5.2x10^3 L

To fill this tank in 238s, the rate must be:

(5.2x10^3 L)/(238s) = 21.8 (L/s) = 1.3x10^3 (L/min)

*** Do you see I do all the unit change?

2. A rectangular piece of plutonium that is 1.5 cm x 3.05 cm x 15 cm is of volume:

1.5 cm x 3.05 cm x 15 cm = 68.6 cm^3

and thus have a mass of:

(68.6 cm^3)*(19.86 g/cm^3) = 1.36x10^3 g

That can generate this much heat per second:

(1.36x10^3 g)*(1.0 joule/s)/(2.8 g) = 0.487x10^3 joule/s

Now convert this to calories per hour:

(0.487x10^3 J/s)*(cal/4.184J)*(3600s/hr) = 4.2x10^5 cal/hr

***You also need to pay attention to the significant figures.  Get it??

Please solve the rest.