Question

Tricky calc 2 question. How do you cut a pizza into 3 slices of equal area with 2 parallel cuts? Radius is 7. I have gotten this far:
I took the integral from 0 to c, of the equation of a circle y=sqrt(49-x^2) and ultimately set it equal to the area of 1/3rd of the Quadrant I quarter.
I solved the integral using trig substitution but end up with an equation that I can't solve for c, without a calculator. WE are supposed to get to an approx. solution without a calculator/graphing calculator.
She said if we get to the point I am at, we have went the wrong way. I'm baffled.
Anyone?

Answer 1

\[1/2(c \sqrt{49-c^2}+49\sin^{-1} (\frac{ c }{ 7 }))=49\pi/12\]the integral solved is:

Answer 2

this came from \[\int\limits_{0}^{c}\sqrt{49-x^2}dx\]
using trig sub x=7sin(theta)

Answer 3

I have an idea, you consider whether that helps or not. I consider just 1/4 of the circle, at quadrant 1 and take integral of the circle from 0 to 7. by that way, i get the area under the curve and divided by 3 to get 1/3 part of that .from that find out the "cut" to improve it into other parts

Answer 4

I actually thought of this, I hadn't executed it tho. The issue is, when I evaluate it, will it give me the point where the cut needs to be made? If not, how do I get the point from what I solve?

Answer 5

A = pi * r^2 = 49 pi
make integral from c to 7 = 49 pi and solve for c

Answer 6

sorry , divide by 3

Answer 7

what? how can I solve it with a c in it? I can't use a calculator

Answer 8

do you try go backward like this: after take integral, you have something and replace 7 and 0 to that to get the answer, now you have 1/3 of Area, get c as POstrOn says you solve for c. I agree with him

Answer 9

hmm, oky, lemme attempt that

Answer 10

find the integral and split it with F(7) - F(c)