Question

Find the area of the shaded portion in the circle.

click pic below

Answer 1

what would the entire area of the circle be?

Answer 2

or rather, do you recall the formula for the area of a circle?

Answer 3

and are we allowed to use trig? cause that top half is looking a little intimidating :)

Answer 4

the angle, formed for the segment, if i did it right; is cos-1(-4/9)

Answer 5

entire area is good to know; but i spose we could do it in parts

Answer 6

or by complements; determin the white area and subtract it from the whole

Answer 7

I would probably go about using simpson's rule for this one... Personally, seems easiest and somewhat accurate.

Answer 8

i dont think her class is into the simpsons rule; unless im confusing the calculus one for something else ...

Answer 9

if we form a right triangle; with hyp = 6 and leg = 3 we get a base of sqrt(27)

the triangle up top then has a base of 2sqrt(7) and a height of 3 giving us an area of 3sqrt(27); then we need to determine the side segments

Answer 10

Simpson's rule isn't overly difficult.
Simspon's rule is.. w/3(x+2E+4O)?
Correct me if I'm wrong?
Split the circle into equal distances of say.. 0.5 and then use simpson's rule..

Answer 11

i couldnt tell you if that would be right or wrong :) cant remember that far back ...

Answer 12

Seems logical, I can't be too sure either.

(0.5/3)((2x3) + (2x11x3) + (4x11x3))
Does this sound right, I couldn't be too sure.

Answer 13

the angle I see formed for the side segments area is: tan-1(3/sqrt(27))

to wit:

area = 6^2 sin(a)/2 ; and 2 sides makes it .... 6^2 sin(a)

36 sin(tan^(-1)(3/sqrt(27))) = 18 really? that was cool

total circle - (3sqrt(27) + 18) if i did it right :)

Answer 14

total area = 36pi ... maybe so

36pi -(3sqrt(27)+18) =abt. 102.5 pi

Answer 15

...... that doesnt make sense lol .... the area would be greater than the whole :)

Answer 16

79.5 would be better if I did it right; but that includes the pi .... so I tried to divide it out and get: abt 25pi :)

Answer 17

is there any way to determine if we got it right? or is there a certain degree of accuracy you are going for?

Answer 18

http://www.wolframalpha.com/input/?i=%2836pi+-%283sqrt%2827%29%2B18%29%29%2Fpi

forgot a paranthesis :)

25.308... pi is my best guess