Question

question 28 of 44
what is the area of the sector shown in the diagram below?
diagram: circle with center c, radius 10 cm, central angle 45° (shaded sector)
options:
a. 11.1 cm²
b. 2.5 cm²
c. 39.3 cm²
d. 50 cm²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \).
Here, \( r = 10\space\text{cm} \) and \( \theta=45^{\circ} \).

Step2: Substitute the values into the formula

Substitute \( r = 10 \) and \( \theta = 45 \) into the formula:
\( A=\frac{45}{360}\times\pi\times(10)^{2} \)
Simplify \( \frac{45}{360}=\frac{1}{8} \) and \( (10)^{2} = 100 \), so the formula becomes \( A=\frac{1}{8}\times\pi\times100 \)
\( A=\frac{100\pi}{8}=\frac{25\pi}{2}\approx\frac{25\times 3.14}{2} \)
Calculate \( 25\times3.14 = 78.5 \), then \( \frac{78.5}{2}=39.25\approx39.3\space\text{cm}^2 \)

Answer:

C. \( 39.3\space\text{cm}^2 \)