Problem: Where would you have to make two parallel cuts on a pizza so that all 3 segments have the same amount of pizza?(adsbygoogle = window.adsbygoogle || []).push({});

Given: the pizza's diameter is 14 in.

Attempt: With the leftmost point of the pizza as the origin of my coordinate system, the equation for the top half of the pizza is y = √7^2 - (x - 7)^2. If I set the integral of that equation from 0 to A equal to one sixth the area of the pizza then A should be how far from the edge of the pizza you'd have to make the first cut, right? I'm just having trouble evaluating this integral. I used a trig substitution x - 7 = 7sinσ and simplified until I had:

(49/2)∫1 + cos(2σ)dσ from (3pi/2) to inversesin(A/7 - 1) which simplifies to

(49/2) * [σ + 0.5sin(2σ)] with the same limits of integration. Plugging the limits into the antiderivative made things real ugly and I can't handle the algebra. Did I make a mistake up to this point? If not, could someone please guide me through the algebra?

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# Use 2 parallel cuts to divide a pizza into 3 segments with equal area

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