Question

a circle is shown.
which expression represents the shaded area formed by sector frg?
a ((3)^2 pi)
b (\frac{45}{360} (3)^2 pi)
c (left( \frac{315}{360}
ight) (3)^2 pi)
d (\frac{(3)^2 pi}{360})

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector of a circle is \( \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify values from the diagram

From the diagram, the radius \( r = 3 \) and the central angle \( \theta = 45^\circ \) for the shaded sector.

Step3: Substitute values into the formula

Substituting \( \theta = 45^\circ \) and \( r = 3 \) into the sector area formula, we get \( \text{Area} = \frac{45}{360} \times \pi \times (3)^2 \), which is \( \frac{45}{360}(3)^2\pi \).

Answer:

B. \(\frac{45}{360}(3)^2\pi\)