Question

Find the area of the shaded sections. Click on the answer until the correct answer is showing.

Answer 1

Do you know how to find the total area of the circle?

Answer 2

yeah. A=2(pi)r^2

Answer 3

Uh, no 2 in front.

\[A = \pi r^2\]gives the area of a circle with radius \(r\)

Answer 4

Okay, do you know how many degrees there are in a complete revolution around the circle?

Answer 5

yeah 360

Answer 6

Good. Then this one's in the bag :-)

If the white region on the right occupies 120 degrees of the 360 degrees in the circle, how much does the white region on the left occupy?

Answer 7

120, so the total area of white is 240 out of 360.

Answer 8

right. so the shaded area is (360-240)/360 of the total area, right?

Answer 9

right, so the area of the shaded region would then come out to, 120?

Answer 10

it's 120 degrees out of the 360. so that means if we know the area of the circle is \(A\), then the fraction of it in the shaded area is \[A*\frac{120}{360} = A*\frac{1}{3} = \frac{1}{3}\pi r^2\]and you just have to plug in the value of \(r\) to get the answer.

Answer 11

it doesnt give me the value of r

Answer 12

look at the diagram again.

Answer 13

it looked like an x. but its 4 sorry.

Answer 14

not a problem...

Answer 15

so it would be
\[\frac{ 1 }{ 3 } {\pi }4^{2}\]

Answer 16

which would equal \[\frac{ 1 }{ 3 }(25)\]

Answer 17

No, \[\frac{1}{3}\pi 4^2 = \frac{16}{3}\pi\]or if you needed a number,\[\frac{16}{3}\pi \approx 16.755\]