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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**