Question

In circle Q with m, angle, P, Q, R, equals, 46, degreesm∠PQR=46
∘
and P, Q, equals, 17PQ=17, find the area of sector PQR. Round to the nearest hundredth.
P
R
Q
Answer
Attempt 1 out of 2

Answer 1

To find the area of sector PQR, we can use the formula for the area of a sector:

\[
\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

where \(\theta\) is the angle of the sector and \(r\) is the radius of the circle.

In this case:
- \(m\angle PQR = 46^\circ\)
- The radius \(PQ = 17\)

Substituting the values into the formula:

\[
\text{Area of Sector} = \frac{46}{360} \times \pi \times (17)^2
\]

Calculating \(17^2\):

\[
17^2 = 289
\]

Now substitute this back into the formula:

\[
\text{Area of Sector} = \frac{46}{360} \times \pi \times 289
\]

To simplify:

\[
\frac{46}{360} = \frac{23}{180}
\]

Now substituting back into the formula:

\[
\text{Area of Sector} = \frac{23}{180} \times \pi \times 289
\]

Now we can calculate the area:

\[
\text{Area of Sector} \approx \frac{23 \times 289 \times \pi}{180}
\]

Calculating \(23 \times 289 = 6647\):

So now we have:

\[
\text{Area of Sector} \approx \frac{6647\pi}{180}
\]

Now approximating \(\pi \approx 3.14159\):

\[
\text{Area of Sector} \approx \frac{6647 \times 3.14159}{180}
\]

Calculating \(6647 \times 3.14159 \approx 20879.49073\):

Now divide by 180:

\[
\text{Area of Sector} \approx \frac{20879.49073}{180} \approx 116.0
\]

Finally, rounding to the nearest hundredth, we get:

\[
\text{Area of Sector} \approx 116.00
\]

Thus, the area of sector PQR is approximately **116.00 square units**.