Question

Find the area of a sector of a circle whose diameter is 16 cm and whose central angle is 63 degrees.
A. 36.2 cm²
B. 35.2 cm²
C. 8.8 cm²
D. 8.36 cm²

Answer 1

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

Answer 2

I like to think of sectors as a sort of percentage of the whole circle, like a pie chart or such.
The 63 degree central angle is part of 360 whole degrees, so the area of the sector is 63/360 of the total area.

Answer 3

0.175?

Answer 4

That would be multiplied onto the total area of a circle, which is given by \( A = \pi r^2 \)

Answer 5

how do I find the radius ? @AccessDenied

Answer 6

You would use the diameter. Diameter is just twice the radius, right?
diameter = 16
radius = 1/2 diameter = 1/2 (16)

Answer 7

Area= 3.14*16^2

Answer 8

Radius is 1/2 (16) = 8, so area uses the 8: 3.14 * 8^2.

Answer 9

3.14*8^2= 200.96 so what do I do next?

Answer 10

This is where I mean to use that fraction 63/360.
63 is the part of the circle we are interested in.
360 is the total circle.
The fraction of the two is basically the percentage of the circle made up by our sector, so 63/360 or 0.175 or 17.5% of the circle is our sector. So 17.5% of the area is the area of our sector.

Answer 11

\( \text{Area of Sector} = \dfrac{63}{360} \times \text{Area of Circle} = 17.5\% \text{ of Area of Circle} \)

Answer 12

ï don't have that as a answer choice.

Answer 13

What did you get? o.o
63/360 * 3.14*8^2

Answer 14

my bad I miss calculated its B. thanks so much!

Answer 15

Yup, glad to help! :)