# Bernd.Group

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How to calculate the surface area of the red part?
>>124689 how is the line calculated? this is too much of a sketch to do anything concrete with
paint and calculate millions of triangles. t. Hauptschulabrecher
>>124689 paint it fully red, then cut it into 1cm wide strips, cut off all the not-red parts and puzzle it together. now you can just measure how long the strip it. it's not exact but who gives a fuck, your teacher is a whore and that's good enough for a whore.
>>124691 I know for a fact it can be done. There is a square, a circle and another line that you can construct using a compass. I don't know how exactly, though. So here would be my actions: 1. Call friend who is getting a phd in mathematics. 2. Describe the problem. 3. Calculate using his instructions. 4. Profit.
>>124689 use integral calculus protip: a circle centered in (0,0) with radius r has formula y = ±√(r²-x²)
>>124700 ok I think it's easiest in this coordinate system the smaller circle has centre in (0,0) and radius 5 5² = y² + x² or y = ±√(5² - x²) the larger circle (well, just the arc) has centre in (0,-5√2) and radius 10 10² = (y + 5√2)² + x² or y = ±√(10² - x²) - 5√2 (the first is implicit formula and the second in explicit formula; in both cases only the +√ branch of the explicit formula, the one in upper semiplane, is relevant) the circles intersect in points where x² is the same in both implicit formulas: 5² - y² = 10² - (y + 5√2)² (y + 5√2)² - y² = 10² - 5² y² + 10√2y + 50 - y² = 75 10√2y = 25 y = 5/2√2 calculating x of intersections: 5² = y² + x² 25 = 25/8 + x² x² = 25(7/8) x = ±5√7/2√2 now you want to integrate between those intersections (from -x to x) the difference between integrals of both circles' explicit formulas: ʃ √(5² - x²) dx - ʃ √(10² - x²) - 5√2 dx indefinite integral of √(r² - x²) you can find in integral tables; (fuck this is getting ugly. you get the idea. if you can't solve it from here on, maybe I go come return and finish it tomorrow. good night bernd.group) (protip: you can integrate only from 0 to x since shape is symmetric, total area is twice that)
you've just ruined 3 hours of my life
>>124709 and i only got as far as figuring out that those ares are equal
13.84% of the square area
>>124719 You must be the smartest Ferret on the earth.
>>124719 ok well tone'd guess I don't have to finish it myself
>>124723 I got afraid when I opened the integral tables and saw arctans
>>124729 Ssb = small box area Ssc = small circle area Sbb = big box area Sbc = big circle area 4Ssb = Sbb 4Ssc = Sbc a + b + c + d = Ssb a + b = Ssb - Ssc c + d = Sbc / 4 = 4Ssc / 4 = Ssc b + c = Ssc c + d = b + c d = b
Just fill the area with water and pour that into a measuring cup. t. physicist
>>124738 oh I see, it's simple the idea is that the small circle has same area as that quarter big circle everything follows straightforwarldy
>>124739 That's the thought I had. t. practical man