Question

A sector of a circle varies directly with the degree measure of its central angle. If a central angle measures 60°, and the area of the sector is 447 ft², what is the area of the sector when the central angle measures 100°?

a. 745 ft²
b. 745.5 ft²
c. 746 ft²
d. 746.5 ft²

Answer 1

The area of the sector when the central angle measures 100° is 745 ft².

Step-by-step explanation:

We are given that a sector of a circle varies directly with the degree measure of its central angle. In other words, as the central angle increases, the area of the sector also increases. We can set up a proportion to find the area of the sector when the central angle measures 100°.

Let A1 be the area of the sector when the central angle measures 60°, and let A2 be the area of the sector when the central angle measures 100°.

Using the given values, we can set up the proportion A1/60 = A2/100. Cross-multiplying, we get A1*100 = A2*60. Since we know A1 = 447 ft², we can substitute it into the equation:

447*100 = A2*60

A2 = (447*100)/60 = 745 ft²

Therefore, the area of the sector when the central angle measures 100° is 745 ft².