This is utterly embarassing but I am completely stupid when it comes to math, especially word problems and the like. No, really. Can someone help me with this seemingly simple math problem? It is not a homework question nor is it a trick question–I am just horrible at math and cannot figure this out to save my life!
Basically, all I need to know is how to find the volume (in cubic yards) of an area that is given in square miles by yards. In other words, I have a word problem that says an enclosure is an area 10 miles square by 10 yards deep and I need to know the volume.
Please do not taunt me mercilessly–just help! This mathaphobia is a real disease!
Bear in mind that it’s really 10 miles by 1 mile by 10 yards, so you’ll need to convert the 10 miles to yards, and the 1 mile to yards. Then multiply the three together for the answer. (note that 10 mi x 1 mi isn’t the only way of reflecting 10 sq miles, but any way you cut that part will get you the same answer.)
Step one: Convert everything to the same units. If you want the answer in yd^3, then the first thing we need to do is convert the miles to yards. Simple enough:
1 mile = 5280ft = 1760 yds.
10 miles, then, is 17,600 yards (1760 x 10)
Step two: Restate the problem with the new units. Now, the problem is this: The enclosure is an area 17,600 yards square by 10 yards deep.
Step three: Crank it out
The volume is simply the area x depth, so all we need to do is this:
17,600 yds x 17,600 yds x 10 yds
Or,
3.1 x 10 ^ 9 cubic yards (The actual answer is 3,097,600,000 yd^3).
But wait… I just re-read you post. And now I am confused
First you say the area is given in square miles, then you say the area is 10 miles square. Those mean two different things (at least to me)! An area of 10 miles square implies that each side is 10 miles long (meaning the area is actually 100 square miles - and the above is the answer). If the area is actually 10 square miles, that’s a bit different:
(10 mi^2) x (1760 yds / 1 mi)^2 = (10 mi^2) x (3,097,600 yd^2 / 1 mi^2) = 30,970,600 yd^2
So, 10 square miles is 30,970,600 square yards.
To get the volume, we simply multiply this by the 10-yard depth:
30,970,600 yd^2 x 10 yd = 309,706,000 yd^3
As you can see, this answer is 100x less than the previous answer.
Anyway, my guess is that you meant the area you are starting with is 10 square miles, so the second answer is the correct one.
Sorry for such a lengthy response to your question.
32 miles square (again, assuming this really means 32 square miles) would be converted to yards the same way. You can treat it as an 8 mi x 4 mi enclosure, convert everything to yards, then multiply everything together:
(8 mi x (1760 yd / mi)) x (4 mi x (1760 yd / mi)) x 10 yd = …
I did indeed put the 6 in the wrong place. Oops. The correct answer was 309,760,000 yd^3. Which is, of course, only 10x less than the previous answer.
And, as I indicated, I would interpret ‘32 miles square’ the same way. But I wasn’t entirely sure whether evilbeth meant ‘32 square miles’ or ‘32 miles square’.
AACCCKKKK! Do I just pick the one that I like since the word problem didn’t give me specifics? Or should I just do it both ways and indicate that the confusion is on the part of the problem-writer?
