To find the area of a sector given the radius and the central angle, we can use the formula:
\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(\theta\) is the central angle (in degrees),
- \(r\) is the radius.
Question 1:
The required area is not provided in your question. Therefore, let's skip to the next questions.
Question 2:
Given:
- Radius \(r = 12\) feet
- Central angle \(\theta = 270^\circ\)
Using the formula: \[ \text{Area of Sector} = \frac{270}{360} \times \pi \times (12^2) \] \[ = \frac{3}{4} \times \pi \times 144 \] \[ = 108\pi \text{ ft}^2 \]
Calculating the approximate value: \[ \text{Area} \approx 108 \times 3.14 \approx 339.12 \text{ ft}^2 \]
So the area rounded to the nearest tenth is approximately: 339.3 ft²
Question 3:
Given:
- Radius \(r = 13\) mm
- Central angle \(\theta = 285^\circ\)
Using the formula: \[ \text{Area of Sector} = \frac{285}{360} \times \pi \times (13^2) \] \[ = \frac{285}{360} \times \pi \times 169 \] \[ = \frac{285 \times 169}{360} \pi \]
Now simplifying \(285 \div 360\): \[ = \frac{285 \times 169}{360} \approx 0.79167 \times 169 \approx 133.33325 \]
Thus: \[ \text{Area of Sector} = \frac{13333}{100} \pi \approx 133.33 \pi \text{ mm}^2 \]
But since the options provided are in terms of π, let's look closer to the options provided. The area can be rewritten with the numbers: \[ \text{Area of Sector} = \frac{285}{360} \times 169 \pi \text{ mm}^2 = \frac{285 \times 169}{360} \pi \]
However, we will check each option against the closest estimates.
Options:
- 40π/3 mm²
- 3211π/24 mm²
- 26π mm²
- 1859π/12 mm²
We obtain: \[ = 133.33 \pi \text{ in terms of π} \]
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1 answer