Question

What is the area of a sector with a central angle of 130° and a diameter of 5.6 in.?

Use 3.14 for π and round your final answer to the nearest hundredth.


Enter your answer as a decimal in the box.


___ in²

Answer 1

Explanation:

The first step is to find the radius of the circle, which is half the diameter:

r = 5.6/2 = 2.8 inThe area of the entire circle is:

A = πr² = 3.14 x 2.8² = 24.616 in²To find the area of the sector, we need to multiply the area of the whole circle by the fraction of the circle represented by the central angle. Since the central angle is 130° out of 360° (a full circle), the fraction of the circle represented by the sector is:

130/360 = 13/36Therefore, the area of the sector is:

A = (13/36) x 24.616 = 8.912 in²Rounding to the nearest hundredth, we get:

A ≈ 8.91 in²Therefore, the area of the sector is approximately 8.91 in².