Question

what is the area of the sector of a circle with θ = 75 degrees and a radius of 4 feet? include pi in your calculation

Answer 1

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

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

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

In this case, \( \theta = 75 \) degrees and \( r = 4 \) feet.

Plugging in the values:

\[
\text{Area of the sector} = \frac{75}{360} \times \pi \times (4)^2
\]

Calculating \( (4)^2 \):

\[
(4)^2 = 16
\]

So now we have:

\[
\text{Area of the sector} = \frac{75}{360} \times \pi \times 16
\]

Now simplify \( \frac{75}{360} \):

\[
\frac{75}{360} = \frac{75 \div 15}{360 \div 15} = \frac{5}{24}
\]

Thus, the area becomes:

\[
\text{Area of the sector} = \frac{5}{24} \times \pi \times 16
\]

Now multiply \( \frac{5}{24} \) by 16:

\[
\frac{5 \times 16}{24} = \frac{80}{24} = \frac{10}{3}
\]

Now we can finalize the area of the sector:

\[
\text{Area of the sector} = \frac{10}{3} \pi \text{ square feet}
\]

So, the area of the sector is:

\[
\frac{10}{3} \pi \text{ square feet}
\]