Question

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)

Answer 1

I WANT CAKE <3

Answer 2

a = area?

Answer 3

if its just the area of the circle, then thats a pretty thin piece of cake...

Answer 4

its hard to determine what "a" is supposed to represent; area, arc length, angle ???

Answer 5

this is what it looks like and a is labelled

Answer 6

ok... is that "a" cm on the radius then?

Answer 7

a = r * sqrt(pi/6) eh.... still not clicking anything useful in me head...srry...

Answer 8

if it is exactly half the area of the sector; the the area of the whole is r^2(pi/6)/2

Answer 9

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))

Answer 10

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

Answer 11

or is "cut in half" mean something else?

Answer 12

cut in half is that line on the pic.
and a cm is half