How many square inches are in a circle whose circumference is 14 inches?

Answer 1

15.6 in2

The circumference is 14 inches use the formula C=2(pi)r to find the radius: 14=2(3.14)r; 14= 6.28r; r=14/6.28 = 2.23

Now use the formula A=(pi)r2 to find the area: A=(pi)r2 = 3.14*2.232 = 3.14*5.198 =15.61.

Using a more accurate value of pi, and using algebra to avoid calculation until the last step gives a more accurate answer, but both answers agree to 1 decimal:

14=2(pi)r => 14=(pi)r => 14/(2*pi)=r => r= 7/pi

A=(pi)(7/pi)2 = (pi)(72)/(pi)2 = (pi/pi2)*49 = 49/pi = 49/3.14... = 15.59...