Question

In circle Q with m, angle, P, Q, R, equals, 86, degreesm∠PQR=86
∘
and P, Q, equals, 10PQ=10, find the area of sector PQR. Round to the nearest hundredth.

Answer 1

To find the area of sector \( PQR \) in circle \( Q \), we will use the formula for the area of a sector:

\[
\text{Area of sector} = \frac{m\angle PQR}{360^\circ} \times \pi r^2
\]

Where:
- \( m\angle PQR \) is the measure of the angle in degrees.
- \( r \) is the radius of the circle.

Given:
- \( m\angle PQR = 86^\circ \)
- \( PQ = 10 \), which is the radius \( r \) of the circle.

Now substituting the values into the area formula:

\[
\text{Area of sector} = \frac{86}{360} \times \pi \times 10^2
\]

Calculating step-by-step:

1. Calculate \( \frac{86}{360} \):

\[
\frac{86}{360} \approx 0.2389
\]

2. Calculate \( 10^2 \):

\[
10^2 = 100
\]

3. The area calculation becomes:

\[
\text{Area of sector} \approx 0.2389 \times \pi \times 100
\]

4. Using \( \pi \approx 3.1416 \):

\[
\text{Area of sector} \approx 0.2389 \times 3.1416 \times 100
\]

5. Calculate \( 0.2389 \times 3.1416 \):

\[
0.2389 \times 3.1416 \approx 0.7505
\]

6. Finally, multiply by 100:

\[
\text{Area of sector} \approx 0.7505 \times 100 = 75.05
\]

Thus, rounding to the nearest hundredth, the area of sector \( PQR \) is approximately:

\[
\boxed{75.05}
\]