Questions: Find the area of the sector of a circle with radius 9 feet formed by a central angle of 70 degrees: square feet Round your answer to two decimal places.

Solution Steps

To find the area of a sector of a circle, we can use the formula: \[ \text{Area} = \frac{\theta}{360} \times \pi \times r^2 \] where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle. Given the radius \(r = 9\) feet and the central angle \(\theta = 70^\circ\), we can plug these values into the formula to find the area.

We are given the radius \( r = 9 \) feet and the central angle \( \theta = 70^\circ \).

The formula for the area of a sector is: \[ \text{Area} = \frac{\theta}{360} \times \pi \times r^2 \]

Substituting \( r = 9 \) and \( \theta = 70 \) into the formula, we get: \[ \text{Area} = \frac{70}{360} \times \pi \times 9^2 \]

First, calculate \( 9^2 \): \[ 9^2 = 81 \]

Next, calculate the fraction: \[ \frac{70}{360} = \frac{7}{36} \approx 0.1944 \]

Now, multiply by \( \pi \) and \( 81 \): \[ \text{Area} \approx 0.1944 \times \pi \times 81 \]

Using \( \pi \approx 3.1416 \): \[ \text{Area} \approx 0.1944 \times 3.1416 \times 81 \approx 49.4801 \]

Rounding \( 49.4801 \) to two decimal places, we get: \[ \text{Area} \approx 49.48 \]

Final Answer