Question

The radius of a circle is 1 mile. What is the area of a sector bounded by a 42° arc?

a) 0.0114 square miles
b) 0.0616 square miles
c) 0.25 square miles
d) 0.0005 square miles

Answer 1

The area of the sector bounded by a 42° arc on a circle with a radius of 1 mile is approximately 0.0114 square miles.

Step-by-step explanation:

To find the area of a sector, we need to know the central angle of the sector and the radius of the circle. In this case, the central angle is 42° and the radius is 1 mile. The formula to calculate the area of a sector is given by A = (θ/360) * π * r², where θ is the central angle and r is the radius.

Substituting the given values, we have A = (42/360) * π * 1² = 0.116 square miles.

Therefore, the correct answer is a) 0.0114 square miles.