anonymous
  • anonymous
sector qs: Charles has a slice of cake; its cross section is a sector of a circle. The radius is r cm and the sector angle is pi/6 radians. he wants to give half of the slice to Jan. He makes a cut across the sector show that when they have half the slice, a=r (sqrt pi/6)
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
I WANT CAKE <3
amistre64
  • amistre64
a = area?
amistre64
  • amistre64
if its just the area of the circle, then thats a pretty thin piece of cake...

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amistre64
  • amistre64
its hard to determine what "a" is supposed to represent; area, arc length, angle ???
anonymous
  • anonymous
this is what it looks like and a is labelled
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amistre64
  • amistre64
ok... is that "a" cm on the radius then?
amistre64
  • amistre64
a = r * sqrt(pi/6) eh.... still not clicking anything useful in me head...srry...
amistre64
  • amistre64
if it is exactly half the area of the sector; the the area of the whole is r^2(pi/6)/2
amistre64
  • amistre64
divide that in half and we get (pi r^2)/24 as the area of each piece. area of a triangle can be found by: (side)(side)(sin(t))/2....which in this case is 2side sin(t)/2 = side(sin(t))
amistre64
  • amistre64
a sin(pi/6) = (pi r^2)/24 a (1/2) (24) = pi r^2 12a/pi = r^2 a = pi r^2/12 really
amistre64
  • amistre64
or is "cut in half" mean something else?
anonymous
  • anonymous
cut in half is that line on the pic. and a cm is half

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