Question

R=3.5cm, angle is 2pie over 7, what is the area

Answer 1

To find the area of a sector of a circle, you can use the formula:

\[
\text{Area} = \frac{1}{2} r^2 \theta
\]

where:
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

In this case, you've provided:
- \( r = 3.5 \) cm,
- \( \theta = \frac{2\pi}{7} \) radians.

Now, substituting the values into the formula:

\[
\text{Area} = \frac{1}{2} \times (3.5)^2 \times \frac{2\pi}{7}
\]

First, calculate \( (3.5)^2 \):

\[
(3.5)^2 = 12.25
\]

Now plug this back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 12.25 \times \frac{2\pi}{7}
\]

This simplifies to:

\[
\text{Area} = \frac{12.25 \times 2\pi}{14} = \frac{24.5\pi}{14}
\]

Now simplify \( \frac{24.5\pi}{14} \):

\[
\text{Area} = \frac{24.5}{14} \pi = \frac{12.25}{7} \pi \approx 1.750 \pi \, \text{cm}^2
\]

Finally, you can compute it numerically:

\[
\text{Area} \approx 1.750 \times 3.14159 \approx 5.50 \, \text{cm}^2
\]

So, the area of the sector is approximately \( 5.50 \, \text{cm}^2 \).