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Can someone help me with this math problem? :(

post #1 of 15
Thread Starter 
Please. Here it is:
Princess Daria demands only the most luxurious of accommodations. So for her bath, she had glacial ice from Antartica shipped to her palace in Egypt. There, the ice was carved into a perfect sphere, exactly 2 meters in diameter. The ice sphere melted into her hexagonal bath measuring 1.5 meters on a side, and 0.8 meters deep.

If the desert heat uniformly melts the surface of the ice at a rate of 1.5mm of depth per minute, how many minutes will it take for her bath to be completely full? Please round up to the nearest minute, and assume the volume does not change between solid and liquid states.

Help
post #2 of 15
I believe you need differential calculus to solve this one exactly.
I'll try it later, after lunch...
post #3 of 15
Quote:
Ice was carved into a perfect sphere, exactly 2 meters in diameter. The ice sphere melted into a hexagonal bath measuring 1.5 meters on a side, and 0.8 meters deep.

The surface of the ice melts at a rate of 1.5mm of depth (read r for radius) per minute, how many minutes will it take for the bath to be completely full? Round up to the nearest minute, and assume the volume does not change between solid and liquid states
AAAAAAHHHHHHHH!!!!!!!!!! Calculus!!!! Related Rates!!!!! ACK! - Wish I'd stayed in class just a little longer to recall this one. I've eliminated some of the unnecessary info. Let me see if I can help you reason through this:

First you need to find the (fixed) volume of the tub.
Then you'll need to find the derivative (the rate of change) of the volume of the sphere (the vol equations are likely printed in an appendix or inside the cover of your textbook). You can plug the 1.5mm (= r) into this derivative equation to find the change of volume/minute (the amt of water per minute).
After this I get a little murky, but there's something about the derivative equation relative to dV/dt, set equal to the volume of the tub, then solve for dt. I truly hope this helps instead of hinders you. Let me know how you fare!!!!!! one step at a time.
post #4 of 15
........sooo hard for my brain......
post #5 of 15
Thread Starter 
AHH to much information!! *brain explodes*
post #6 of 15
Have you tried doing a search for a maths or calculus forums? I'm sure some of the members there would be able to help you out
post #7 of 15
Ahhhhhhhhhhhhh anything to do with math scares me!!!
post #8 of 15
Quote:
Originally Posted by Cabbit
AHH to much information!! *brain explodes*
OK, so I should have made my first sentence "One step at a time!"

1st: Find the area of the hexagon here (about halfway down) and then multiply by 0.8 (the depth of the tub) to get the volume of the tub.

Does that make sense so far?
post #9 of 15
Quote:
Originally Posted by m_brane
I believe you need differential calculus to solve this one exactly.
I'll try it later, after lunch...
Okay, I'm back to give it a try (did not need differential calculus afterall):



then go to

http://www.akiti.ca/Quad3Deg.html

and solve the cubic equation for "t" numerically (after putting in the volume of the hex tub, ice sphere, etc.). Let me know if this is correct (assuming this is some homework problem that you will have the answer later).
post #10 of 15
OK, if that's NOT differential calculus, then what kind of calculus IS it??????? I've done related rate problems in my Calc 1 course last semester in college - I thought that WAS differential calculus (you know, dV/dt - the differential)??
post #11 of 15
Quote:
Originally Posted by RicaLynn
OK, if that's NOT differential calculus, then what kind of calculus IS it??????? I've done related rate problems in my Calc 1 course last semester in college - I thought that WAS differential calculus (you know, dV/dt - the differential)??
Erica, sorry, I meant the problem didn't need a differential equation...just a bunch of algebraic steps with calculus thrown in. Hope it is at least close as I haven't done this for years. What is a Calc 1 course? Sounds from your earlier post that you enjoyed it.
post #12 of 15
OH, ok that makes more sense. I actually retook my 1st semester of calculus (Calc 1) last spring because it had been, ahem, 13 years! since I'd taken it the first time. I enjoyed both, but I knew I would need the refresher for my chemistry and other science classes. I'm studying to enter Pharmacy school in a year or so.
post #13 of 15
Quote:
Originally Posted by m_brane
Okay, I'm back to give it a try (did not need differential calculus afterall):


then go to

http://www.akiti.ca/Quad3Deg.html

and solve the cubic equation for "t" numerically (after putting in the volume of the hex tub, ice sphere, etc.). Let me know if this is correct (assuming this is some homework problem that you will have the answer later).
I got 1000 min after plugging in the numbers. Cubic equation gives 3 mathematical roots but if you look at the problem the volume of the ice sphere is smaller than the volume of the hexagon tub to 0.8 m so there is no physical answer to the original problem--you could melt all the ice and not fill the tub to 0.8 meter depth.
post #14 of 15
'all are makin my brain hurt...Just tell the snooty woman to shut up and take her dang bath and dont worry about the blasted water..It's Wet!!! Nuff said...lol
post #15 of 15
Quote:
Originally Posted by Cabbit
Please. Here it is:
Princess Daria demands only the most luxurious of accommodations. So for her bath, she had glacial ice from Antartica shipped to her palace in Egypt. There, the ice was carved into a perfect sphere, exactly 2 meters in diameter. The ice sphere melted into her hexagonal bath measuring 1.5 meters on a side, and 0.8 meters deep.

If the desert heat uniformly melts the surface of the ice at a rate of 1.5mm of depth per minute, how many minutes will it take for her bath to be completely full? Please round up to the nearest minute, and assume the volume does not change between solid and liquid states.

Help
Good Lord. Calculus! That takes me back a LONG time. I was never very good at it in highschool (would have helped I'm sure if I had have studied AT ALL...lol) and so I would be of even less help now...sorry! My mum's a maths teacher though...I'll ask her and we'll both learn something!!
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