Question

Last year, Bob's Auto Supplies sold 120 air filters out of a total of 3000 items sold. Bob will show his sales in a circle graph. Find the measure of the central angle that will represent the air filter category.

Answer 1

Assuming that bob will use a circle with radius 1 unit,
then the area of the whole circle is A = pi R^2
A = 3.1416(1^2)
A = 3.1416

fraction of auto supplies = 120 / 3000 = 0.04
Area auto supplies = 3.1415(0.04) = 0.1257

formula for of a circular segment
A = 0.5r^2x
where x is the angle in radian
0.1257 = 0.5(1^2)x
x = 0.2513 rad
convert to degrees
x = 0.2513 rad ( 180 /pi)
x = 14.40 degrees