Any math wizzes out there?

[spedbug]

I scraped through geometery, barely, years ago. SFB isn't getting any help from me. Perhaps one of you nice people can help?

Comments

[spedbug.livejournal.com]

How, exactly, is she supposed to determine the sloping 4' of volume? Does she find volume of 3x20x24 and then an additional 3x20x14?

[(Anonymous)]

Divide it into square chunks, 3x20x10 = 600 for the shallow end. 6x20x10 = 1200 for the deep end. the square section above the slope is 3x20x4 = 240. the bit that includes the slope will be 3x20x4 divided in half = 120.

The total is 2160 cubic feet, or 16119.4 gallons.

[angstzeit.livejournal.com]

I come up with 2160 cubic feet and 16119.402985074626865671641791045 gallons.
But what the hell do I know?

[resqgeek]

I would break the volume into three sections:

3x20x24 for the shallow water

3x20x10 for the deep water

and a trigular prism piece for the sloped portion equal to 1/2 of 4x3x20

Total volume is 1,440 + 600 + 120 = 2,160 cu. ft.

Divide by 0.134 to get gallons give us 16,119.4 gallons

[amyleaton.livejournal.com]

I never, NOT ONCE, learned about PRISMS in geometry. So I would hire a contractor to build the pool then fill it up and see how much water you used... Guess that doesn't really help, glad you found others who could! :-)

Oh, the pic refers to me, not you!

[thescrappycat.livejournal.com]

This is the kind of thing that makes me run away screaming.

[miketroll.livejournal.com]

The answers and explanations everyone has offered look fine and relate to the diagram. I just have one small problem remaining with the question: what does it mean by "with concave hexagonal bases"? If you can get the answer without this information, why add it?

[mlbish.livejournal.com]

I always loved problems like that where you had to break the object of interest up into chunks to figure out the total volume. For some reason, I find them so satisfying.... :-)

I didn't calculate it for you (mostly because I can't remember how to calculate the volume of a triangle shape) but it looks like you've had plenty of help.

[myopicmeringue.livejournal.com]

You can also do it by imagining that it was a whole cuboid (20 x 24 x 6) and then take away the missing part ((3 x 10 x 20) + (3 x 4 x 20)/2) from that. I find that way slightly easier, because I find it fiddly to divide the swimming pool into chunks. :-)