Question

The arc corresponding to a central angle of 35 degrees in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.

Answer 1

Find the circumference of a circle with radius 10 feet. \(C = 2\pi r\)

Find the fraction of that circumference that represents 35 degrees, if the entire circle is 360 degrees.

Answer 2

\[C=20\pi\]

Answer 3

Okay, now find the fraction of \(20\pi\) that represents 35/360 of the total.

Answer 4

I don't know how to do that

Answer 5

If I told you to find the fraction of \(20\pi\) that represents 1/2 of the total, could you do that?

Answer 6

If you get the answer to this problem correct, you are paid $1000 by your teacher. My fee for helping you is 1/2 of what you get. How much will I get?

Answer 7

$500

Answer 8

Okay. If I get 3/4 of what you get, how much will I get?

Answer 9

$750

Answer 10

Right. So you understand the concept, whether you realize it or not. What is 35/360 of \(20\pi\)?

Answer 11

6.19?

Answer 12

Close: I get 6.1086. I wonder if you made a mistake while rounding? 6.1086 rounded to two decimal places would be 6.11. The 0 is the place where we are rounding, so we look one digit to the right. If that digit is 0-4, we keep the 0 we have in our rounding spot, otherwise we add 1 to the rounding spot's digit (and if that produces a carry, we have to propagate that to the left — 5.996 would round to 6.00 if rounding to two decimal places).

Answer 13

Yea, I messed up the rounding.