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

1 answer

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 \( 5.50 , \text{cm}^2 \).