Help with conversions?

Question

Hi, I'm having trouble figuring out how to do this problem, my answers are all over the place, can anyone help me?

About two centuries ago, Benjamin Franklin showed that 1 teaspoon of oil would cover 0.5 acres of still water. If 1.0 x 10^4 m^2 = 2.47 acres and there is approximately 5cm^3 = 1 teaspoon, calculate the thickness of the layer of oil.

Answer 1

You need to cover the entire area, 1.0 x 10^4 m^2 with oil.

When you take area x thickness, you get volume. 5cm^3.

So...

Let's first convert the area, m^2, to cm^2. I'm doing this to get the units the same.

You surely know how many cm are in a meter... 100 cm = 1m

Now, how many cm are in a square meter? Well, 1 m x 1m = 1 m^2, therefore 100 cm x 100 cm = 10,000 cm^2 (Same as one square meter)

1.0 x 10^4 m^2 (10,000 cm^2 / 1 m^2) = 100,000,000 cm^2

or...1.0 x 10^8 cm^2

Note that in the previous calculation, I canceled the m^2.

So, 1.0 x 10^8 cm^2 = 2.47 acres.

But, we want to know what thickness will cover just .5 acres...per Ben's calculation. Or at least verify that one teaspoon of all, albeit very small, could do the job.

2.47 / x = .5
x = 1.235

So, we need to divide that 2.47 acres by 1.235 in order to get the number of cm^2 in one half acre.

1.0 x 10^8 cm^2 / 1.235 = 80,971,659.9 cm^2

Now we have 5cm^3 of oil.

What thickness (X) will we need to multiply the previous answer (which is an area) to get 5cm^3??

5 cm ^3 / 80,971,659.9 cm ^2 will yield X cm (or the thickness)

6.17500 x 10^-8 cm of oil is the thickness.

Of course, you can start to multiply by multiples of 10 to get mm or micrometers etc.

Hope that helped.

Regards,

Mysstere