Convert sunlight to electricity in a given area

[Revicted]

Homework Statement

Question: Lake Mead is formed by the Hoover Dam, and while it actually changes in area and volume, consider it has an average area of 100,000 acres. Assume that 250 W/m^2 of sunlight falls on Lake Mead, how much electricity could be produced if this lake area was covered by solar voltaic cells that convert sunlight directly to electricity with 15% efficiency?

Homework Equations

1 Acre = 4046.85642 Square Meter

The Attempt at a Solution

I am trying to find the amount of electricity that could be produced in this area, so I know that the final answer needs to be in Watts. This means I need to find a way to cancel out the m^2 in a conversion.

Here is the conversion I attempted to cancel out the acres and square meters:
(100,000 acres)*(4046.85642 m^2)*(250W) = 1.012*10^11W

That number is assuming 100% efficiency. So to account for the 15% efficiency of the solar panels:
(1.012*10^11)/.15 = 6.74*10^11W

I don't feel very confident in this answer, but I'm not quite sure what I am missing or what I am doing wrong. Any nudges in the right direction would be greatly appreciated!

 

[Orodruin]

You are essentially correct with one minor issue in a middle step: The units in the middle of your computation. The conversion factor should be 1 = 4046 m^2/acre and the power per area should have units of 250 W/m^2. In general you can treat units exactly like you do variables to find out the unit of a product or division. Since 4046 m^2 is 1 acre, 4046 m^2/1 acre = 1 acre / 1 acre = 1 and you can multiply anything with it and get the same thing.

 

[Revicted]

Oh yes, sorry, I left that out on here. That is actually how I have it written out in the conversion on my paper in order to cancel out the units. Otherwise everything looks correct?

 

[Orodruin]

I am trying to find the amount of electricity that could be prodThat number is assuming 100% efficiency. So to account for the 15% efficiency of the solar panels:
(1.012*10^11)/.15 = 6.74*10^11W

Sorry, I missed this at first read through. The 15% efficiency means you only get 15% of the power out of the system. You therefore need to multiply by 0.15 rather than divide by it. Otherwise it is what I would have done assuming the actual numbers are correct.

 

[Revicted]

Makes sense. Not sure why I divided there. Thanks so much!