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Question

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What is the diameter of the pizza, in millimetres? Please round to the nearest millimetre.

Answer 1

Poker Card 140 mm by 70 mm

Let the radius of the pizza be r.

r^2 = (r-70)^2 + (r-140)^2

r^2 = r^2 - 140r + 4900 + r^2 -280r + 19600

r^2 - 420r + 24500 = 0

r = [420 +/- sqrt((420)^2 - 4(1)(24500))]/(2(1))

r = [420 +/- sqrt(176400 - 98000)]/2

r = 210 +/- sqrt(78400)/2

r = 210 +/- 140

Take possible solution:

r = 350 mm

Therefore the diameter of the pizza is

diameter = 2 x r

= 700 mm

Answer 2

The radius is 5 times the length of the shorter side of the rectangle, or 350 mm. No rounding is needed. The answer is exact and can be found from algebra.

The formula for a circle is

x^2 + y^2 = r^2

We are given one point on the circumfrence of the circle,

(r - 140, r - 70)

Stick those values in for x and y and solve. You get r = 350. The diameter is thus 700 mm.

You can "normalize" the problem and simplify the computation. Say that the card is 1" x 2" instead of 70mm x 140mm. The radius of the circle comes out, with much simpler computation, as 5".

Answer 3

Using the upper left corner of the box as the center of
your typical x,y co-ordinate system, the pizza center is
at point r,-r and as a circle, the pizza is defined by
(x-r)^2+(y+r)^2=r^2. Expanding , we have
x^2-2xr+r^2+y^2+2yr+r^2=r^2. Now we have a point on
the circle 140,-70 which we can substitute for x,y in the
above equation. But for simplicity let's scale it down to
2,-1. Then we get 4-4r+r^2+1-2r+r^2=r^2 and simplifying
we have r^2-6r+5=0. Solving for r quadratically we get 5 and 1. Throw out 1 as merely hypothetical ,use 5 and
scale back up so that 5 becomes 350. That's r, so
the diameter is 700. Nice puzzle.

Answer 4

If the pizza maker is serious about custumer satisfaction, then he should be concerned with the capability of an average person's ability to hold a slice of pizza in his/her hand. A person usually hold a slice of pizza by placing his thumb and forefinger at the ends of the arc of a slice of a pizza (so he can have a first bite with the corner part of the slice.) So a pizza maker should not be making slices that will result to arcs bigger than this.

Because of the above consideration, the diameter of the pizza will depend on the arc of one slice that can be accommodated by the span of an average customer

Answer 5

hehe nice one. isn't it 700? No joke, I copied it into paint, and counted the pixels of the card deck. It's 20 X 40 Pixels which is equal to 70mm by 140mm so the scale is 3.5 mm for every 1 pixel. then i just counted the length of the pizza box. Simplest way is usually the best, plus its 2 am gimme points. :) I'm not good at arc angle geometry.

Answer 6

the given 70*140 mm can b converted to 1*2 in some unit say x.

1 x unit=70 mm.

(r-1)^2+(r-2)^2=r^2.

here, r=5 is the solution in unit x.so in mm it is 350.

Answer 7

1400 mm

Answer 8

i'm gonna go with 700mm, just like everyone else that did the math got.... hehehe

Answer 9

2 milliweiners long

Answer 10

700mm