Vertical cuts of a circle

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xXMARKXx

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Feb 14, 2007
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You and your friends decide to cut a 12-inch diameter, round pizza into 3 slices of equal area by using vertical cuts. Write an integral to determine where the cuts should be made, tell which technique could be used to integrate it, and then use a calculator to compute the answer. (put on a coordinate grid)

(its basically a circle with two vertical cuts down the center...making 3 equal areas)

thanks guys
 
Maybe you could use polar integration. If this is what you are meaning.

Each slice will be 120 degrees.

\(\displaystyle \L\\\frac{1}{2}\int_{0}^{a}6^{2}d{\theta}=12{\pi}\)
 
area of the circle is \(\displaystyle \L 36\pi\).

center the circle at the origin ... the equation would be x<sup>2</sup> + y<sup>2</sup> = 36

\(\displaystyle \L 2 \int_a^6 \sqrt{36 - x^2} dx = 12\pi\)

use trig substitution ... \(\displaystyle \L x = 6\sin{\theta}\) ... for the integration.

solve for "a" ... because of symmetry, the other cut will be at x = -a.
 
do you know the answer then, because we havn't really been taught that yet...
 
bummer.

guess you'll have to use guess and check with your calculator since you are allowed to use it.
 
Are you familiar with integration at all?. Otherwise, why would you be assigned an integration problem?.

Try it in polar as I posted. No trig sub involved.
 
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