Question: The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6. The estimated value of is 3.14. The measure of the angle subtended by the arc is ?°
Answer: A=pr^2, C=2pr, a/360=6p/C solving each step-wise and substituting them into the next equation...solve for r first from the Area equation...
r=(A/p)^(1/2) using this in C
C=(4Ap)^(1/2) using this C in the last equation...
a/360=6p/(4Ap)^1/2)
a=2160p/(4Ap)^(1/2)
a=(4665600p^2/(4Ap))^(1/2)
a=(1166400p/A)^(1/2)
We are told A=78.5 and p=3.14 so
a=(3662496/78.5)^(1/2)
a=46656^(1/2)
a=216 degrees
