SOLUTION: I have to construct a figure that can hold 100 mm cubed of water. I can't figure out how to find the easiest measurements to construct this. I am doing a cone so the formula is V=1

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Question 198016: I have to construct a figure that can hold 100 mm cubed of water. I can't figure out how to find the easiest measurements to construct this. I am doing a cone so the formula is V=1/3*pi*radius squared*height. Please help! thanx!
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To get a volume of 100 mm2, suppose I have a
box that is 10 mm high. Now suppose it has a square base
The area of this square base has to be 10 mm2
That means each side has to be sqrt%2810%29 since
sqrt%2810%29%2Asqrt%2810%29+=+10
To get the volume,
sqrt%2810%29%2Asqrt%2810%29%2A10+=+100 mm3
Now the question is, How do I construct a side sqrt%2810%29 mm
long? I know that a right triangle, with sides = 1 and 3.
The diagonal is sqrt%281%5E2+%2B+3%5E2%29, which equals
sqrt%2810%29. Use that diagonal to make the sides of the base.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If you are going to construct a cone, then you are going to lay out a circle on your material whose radius is the height of the cone. So pick something convenient, like 10 mm. Realize, of course, that this is going to be a very small object once you have constructed it. If it were a cube, it would be less than half a centimeter on a side. A sphere would be a tiny bit larger than the smallest pearls in a pearl necklace. You get the idea.

So, having chosen 10 mm for the height, we can now look at the volume formula:



But if the height is 10 mm, then:









Now we can calculate the circumference of the base.



Now, mark point 1 on the circumference of your circle of material. From that point, measure around the circumference 19.4 mm and mark point 2 (you might want to go a little farther so that you have some overlap when you form the cone). Construct two radii at points 1 and 2. The circle sector from point 1 to point 2 will form your cone. Make cuts along the two radii and keep the piece that is 19.4 mm along the arc edge. Roll your material into a cone shape and attach the two radius edges together (using the overlap you accounted for earlier).

Et Voila!

If you are really going to do this, I would tell your instructor that you are going to make something that has 100 cubic centimeters volume so that the construction won't be something so small it is hardly possible to manipulate. A cone with 100 cc volume and 10 cm height would be about 5 inches tall and roughly 3 inches across the base.


John