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Volume of "cone" with flat top

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by beboppin » Tue Aug 11, 2009 8:18 pm
How would you guys calculate the volume of a cone, but with part of the top cut off flatly? I thought of 2 ways although they aren't tying out with each other, so I may be missing something.
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difference of two cones

by Gelopzwewr » Tue Aug 11, 2009 10:55 pm
The volume of a partial cone is the same as the volume of the full large cone minus the volume of the "smaller cone" that is the missing portion. You can also use integral calculus to figure it out.
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by beboppin » Wed Aug 12, 2009 3:18 am
Would it also be possible to think of the shape as a cylinder plus cone? That is, you have a regular cylinder in the center, and when you take that out, you are left with a cone that effectively has a hole bored through the middle and expanded. It makes sense conceptually to me but I cannot get them to equal. Would appreciate any help on this.
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Re: Volume of "cone" with flat top

by sreak1089 » Wed Aug 12, 2009 3:39 am
It depends on the information given. I would do it this way.

1. Find the volume of the original cone, with out the actual top part cut cut off flatly.

2. Find the volume of the cone (the part that will be cut off).

3. Subtract # 2 from # 1.
beboppin wrote:How would you guys calculate the volume of a cone, but with part of the top cut off flatly? I thought of 2 ways although they aren't tying out with each other, so I may be missing something.
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