Question

find the area of a sector of a circle having radius r and central angle θ.
r = 12.6 cm, θ = 63°

the area is approximately □ cm².
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values

We are given \( r = 12.6\space\text{cm} \) and \( \theta=63^{\circ} \). Substitute these values into the formula:
\( A=\frac{63}{360}\times\pi\times(12.6)^{2} \)
First, calculate \( (12.6)^{2}=12.6\times12.6 = 158.76 \)
Then, \( \frac{63}{360}=\frac{7}{40}=0.175 \)
So, \( A = 0.175\times\pi\times158.76 \)

Step3: Calculate the value

First, multiply \( 0.175\times158.76=27.783 \)
Then, multiply by \( \pi \): \( A = 27.783\times\pi\approx27.783\times3.1415926535\approx87.3 \) (rounded to the nearest tenth)

Answer:

\( 87.3 \)