if cutting a central cross section of a cone yields an angle of 22 degrees at its point, what does the height have to be to hold 2 ounces or 3.6 cubic inches of water? I believe the answer should be done by solving for the integral of the circle area over the height.
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You should be able to avoid integration by using trig functions. Use your angle to find the ratio of the height to the base's radius (say $2:1$). Once you have this, set this up as $x*2x$ and let it equal $3V$, where $V$ is volume. – Leonidas Lanier Aug 25 '15 at 16:23
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You only need integration if you want to derive the formula for the volume of the cone. Otherwise, you can just use the formula. – jxh Aug 25 '15 at 16:31