To calculate the area of a sector of a circle, you can use the formula:
\[ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 \]
where \(\theta\) is the angle in degrees, and \(r\) is the radius.
In your case, the central angle is 30 degrees and the radius is 5 inches. Plugging these values into the formula gives:
\[ \text{Area of sector} = \frac{30}{360} \times \pi (5^2) \]
This can be simplified to:
\[ \text{Area of sector} = \frac{30}{360} \times \pi \times 25 \]
Now, let's look at the options provided:
- \(\pi(5 \text{ in}) \frac{30}{360}\)
- \(\pi(5 \text{ in}) \frac{230}{360}\)
- \(\pi(30 \text{ in}) \frac{25}{360}\)
- \(\pi(30 \text{ in}) \frac{5}{360}\)
The first option involves the correct radius (5 inches) and the central angle (30 degrees), but doesn't include the square of the radius.
Thus, the correct formulation that closely resembles our derived formula is:
Option 1: \(\pi(5 \text{ in}) \frac{30}{360}\) (but missing the radius squared).
However, strictly speaking none of the options perfectly fits the correct area formula; hence, option one contains the correct angle and radius, albeit in the wrong context.
You would typically find the necessary area using something akin to:
\(\frac{30}{360} \times \pi (5)^2\). However, if you must choose one from the options, option 1 is the best representation of the sector area with the correct angle and radius consideration, but keep in mind it's not exactly formatted for the area specifically. If you're restricted to choosing from the exact options, note they're not fully accurate.
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