Question

how would i do this problem?

Answer 1

You are given a circle with an arc of length of 4.82 in. The sector which intercepts this arc has a central angle of 65 degrees. You are looking for the circumference of the circle.
Is the above correct?

Answer 2

yes that is correct

Answer 3

so you would step it up like this right ? 4.82 = 65/360 and get 26.69?

Answer 4

set*

Answer 5

The circumference of a circle is

\(\large C = 2 \pi r \)

This is for a full circle with a central angle of 360 degrees.
For a sector of a circle, the length of an arc is a fraction of the full circumference.

\(S = \dfrac{n}{360^\circ} \times 2 \pi r\)

S = arc length
n = central angle measure

Answer 6

You are on the right track.
65/360 is part of it.
Use 65/360 for n/360 in the formula.

Answer 7

\(S = \dfrac{n}{360^\circ} \times 2 \pi r\)

Your arc length is given as 4.82 in., so you can substitute that for S:

\(4.82 ~in. = \dfrac{65^\circ}{360^\circ} \times 2 \pi r\)

Now you have only one unknown, the radius.

Solve the equation for r.
Then just use

\(C = 2 \pi r\) to find the circumference of the circle.

Answer 8

Oh, I see what you did.
That was very good.
If 4.82 in. is 65/360 of the circumference, then you can solve it more easily without having to find the radius.

\(4.82 ~in. = \dfrac{65}{360} C\)

\(C = 4.82~in. \times \dfrac{360}{65} \)

\(C = 26.70~in.\)

Answer 9

You are correct.

Answer 10

oh yes! thanks

Answer 11

You're welcome.