Question

An arc length 5 feet subtends central thetaa,in a circle with a piameter 7 feet.
a)Determine the area of the exact radian measure of theta
b)Determine the area of the sector with central angle theta
c)determine the peremeter and the sector

Answer 1

What is the circumference of the circle?

Answer 2

360 degrees

Answer 3

Circumference of a circle is pi times diameter. What is the circumference of the circle?

Answer 4

pie r ^2?

Answer 5

\[C=\pi d\]

Answer 6

is d diameter?

Answer 7

yes. Didn't you read what I wrote earlier: Circumference of a circle is pi times diameter.

Answer 8

yea i am just making sure

Answer 9

so c would be pie7

Answer 10

Yes. The circumference is 7 pi.

Answer 11

What is the measure of the arc according to the problem?

Answer 12

the arc is 5 feet

Answer 13

So the arc is this fractional part of the circle:
\[\frac{5}{7\pi}\]

Answer 14

Do you understand that?

Answer 15

yes i do

Answer 16

I see that you know a circle is 360 degrees. How many radians is a circle?

Answer 17

ummmm im not sure is it 4

Answer 18

360 degrees = 2 pi radians

Answer 19

aw k i didnt know

Answer 20

So a circle is 2 pi radians. So find theta. It is:
\[\frac{5}{7\pi} \times 2\pi \]

Answer 21

it =10