[artwill872]

An oil spill released 4.9 millions barrels (1 barrel = 42.0 gallons) of oil. Half of the oil was found on the surface while the rest exists as plumes near the ocean floor. Assuming exactly half of the spilled oil settled at the surface (in a perfect circle) and the thickness of the spill was 3 mm, what would be the diameter of the spill in meters?


So I have volume and the measurement of one dimension of the circle. I have to end up with a measurement in meters, so I start the set up like this:

4.9 x 10⁶ barrels * 42 gallons / 1 barrel * 3.785 Liters / 1 gallon * 1000 mL / 1 L * 1 cm³ / 1 mL * 1000mm³ / 1cm³

This seems to make sense to me so far. I took the volume and got to a measurement in mm. I'm not sure what to do with the 3mm in the problem. Assuming my set up to this point is correct, then there should only be one or two more steps. I've been trying to guess my way to the right answer and I've tried several things, not knowing whether or not they made any sense, and I still haven't managed to get there. What am I missing?

I know the right answer is 1.29 x 10⁴ m

[rabolisk]

From geometry, you should remember that volume = area * height (i.e. length, thickness). The next step is to remember the relationship between the diameter and the area of a circle.

[artwill872]

From geometry, you should remember that volume = area * height (i.e. length, thickness). The next step is to remember the relationship between the diameter and the area of a circle.

Ok, I looked these up and did this:

I divided the volume (7.78953 x 10¹⁴ mm³) over the height (3 mm) to find the area.

Then I divided the area by pi to find the radius squared.

Then I took the square root of the radius and multiplied it by 2 to find the diameter.

My answer is way off, at 1.8 x 10⁷ mm.

I'm not sure what else to try but I'm going to keep playing with the numbers. Maybe I miscalculated something early on. Did I follow your instructions properly?

[artwill872]

Actually, it's not "way off".. it's much closer to the correct answer than I've been able to get so far.

The right answer is 1.29 x 10⁴ m

and I'm at 1.8 x 10⁴ m

[rabolisk]

Read the problem carefully again. Your approach is correct though.

[artwill872]

Read the problem carefully again. Your approach is correct though.

Thanks, rabolisk.

Here is what I did this time:

First of all, I forgot to take only 1/2 of the volume earlier! So after discovering this silly mistake, I took the volume in mm² and divided by the thickness in mm to get the area in mm², which came out to 1.29 x 10¹⁴ mm².

I divided the area by pi to find the radius squared, which is 4.13 x 10¹³ mm².

Then I took the square root of this number and multiplied it by 2 to find the diameter, which came out to 1.29 x 10⁷ mm.

Then converted into meters and got my answer