Question

What is the area of a sector with a radius of 3 cm and a central angle of 49 degrees? Correct to 3 significant figures.

A) 2.37 cm^2
B) 4.42 cm^2
C) 5.28 cm^2
D) 6.33 cm^2

Answer 1

The area of a sector with a radius of 3 cm and a central angle of 49 degrees is 3.82 cm² when rounded to three significant figures. The provided options do not contain this value, suggesting an error in the options.

Step-by-step explanation:

The area of a sector can be calculated using the formula A = πr² (θ/360), where A is the area, π is pi (approximately 3.1415927), r is the radius of the circle, and θ is the central angle in degrees. In this case, we have a radius of 3 cm and a central angle of 49 degrees. Let's calculate the area:

A = π * (3 cm)² * (49/360) = 3.1415927 * 9 * (49/360)
= 3.1415927 * 9 * 0.1361111 = 3.8156761 cm²

However, we must express the answer to three significant figures. So, the result will be rounded to 3.82 cm². None of the options provided match this correct result, so possibly there is an error in the options given.