Question

Find the length of the arc for a circle with a radius of 7 yd and a central angle of 105degrees leave your answer in terms of pi

Answer 1

To find the length of the arc of a circle given the radius and the central angle, you can use the formula:

\[
L = r \theta
\]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.

First, we need to convert the central angle from degrees to radians. The conversion formula is:

\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]

For an angle of 105 degrees:

\[
\theta = 105 \times \frac{\pi}{180} = \frac{105\pi}{180} = \frac{7\pi}{12}
\]

Now that we have the angle in radians, we can substitute the radius and the angle into the arc length formula:

\[
L = 7 \times \frac{7\pi}{12}
\]

Calculating this gives:

\[
L = \frac{49\pi}{12}
\]

Thus, the length of the arc is:

\[
\frac{49\pi}{12} \text{ yards}
\]

This is the answer in terms of \(\pi\).