18 April 2006

Math teacher + mom = crazy delicious geometry problems!

An email from my mom:
The problem below is being used in geometry and we're trying to figure it out. The answer is 1/27 pi h-cubed. We have no idea how they got that. Do you know?

Water is being stored in a conical tank with height 12 feet and base diameter 8 feet. Write an expression for the volume of water in the conical tank as a function of h, the height of the water in the tank.
This is a pretty good problem. Feel free to give it a shot in the comments. The only further information you need is that the volume of a right circular cone with base radius r and height h is (1/3)*pi*(r^2)*h.

First hint: the answer above is wrong.


Blogger Bruce said...

The above answer is the volume of the given cone (full) where height = base radius x 3.

For water level at height = h, I subtracted the volume of the air space from the full volume of the cone and got


Unless I screwed something up, in which case, please disregard that answer.

11:47 AM  
Blogger Mrs. Peel said...

Yep, that's right. The teachers were able to figure out where the book's answer came from (the book had defined h as the distance from the top of the tank to the water level, rather than the height of the water as it claimed), but they (and the book) forgot to subtract that volume from the total volume of the tank. So the book was wrong on multiple counts. I was amused.

Thanks for stopping by.

1:38 PM  

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