Math worksheet for calculating the area of a sector of a circle using the formula (central angle/360) × π × r².

Let's solve each problem step by step using the formula for the area of a sector:

$$
\text{Area of a sector} = \frac{\text{central angle}}{360^\circ} \times \pi \times r^2
$$

We’ll use $ \pi = 3.14 $ and round answers to two decimal places.

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🔹 Problem 1:

- Radius $ r = 8 $ cm
- Central angle = $ 90^\circ $

$$
\text{Area} = \frac{90}{360} \times 3.14 \times 8^2 = \frac{1}{4} \times 3.14 \times 64 = 0.25 \times 3.14 \times 64
$$
$$
= 0.25 \times 200.96 = 50.24 \, \text{cm}^2
$$

✔ Answer: 50.24 cm²

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🔹 Problem 2:

- Radius $ r = 18 $ ft
- Central angle = $ 130^\circ $

$$
\text{Area} = \frac{130}{360} \times 3.14 \times 18^2 = \frac{13}{36} \times 3.14 \times 324
$$
First calculate $ 3.14 \times 324 = 1017.36 $

Now $ \frac{13}{36} \times 1017.36 \approx 0.3611 \times 1017.36 \approx 367.57 $

✔ Answer: 367.57 ft²

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🔹 Problem 3:

- Radius $ r = 19 $ cm
- Central angle = $ 240^\circ $

$$
\text{Area} = \frac{240}{360} \times 3.14 \times 19^2 = \frac{2}{3} \times 3.14 \times 361
$$
$ 3.14 \times 361 = 1133.54 $

Now $ \frac{2}{3} \times 1133.54 \approx 0.6667 \times 1133.54 \approx 755.69 $

✔ Answer: 755.69 cm²

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🔹 Problem 4:

- Radius $ r = 22 $ ft
- Central angle = $ 110^\circ $

$$
\text{Area} = \frac{110}{360} \times 3.14 \times 22^2 = \frac{11}{36} \times 3.14 \times 484
$$
$ 3.14 \times 484 = 1519.76 $

Now $ \frac{11}{36} \times 1519.76 \approx 0.3056 \times 1519.76 \approx 463.64 $

✔ Answer: 463.64 ft²

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🔹 Problem 5:

- Radius $ r = 3.5 $ m
- Central angle = $ 100^\circ $

$$
\text{Area} = \frac{100}{360} \times 3.14 \times (3.5)^2 = \frac{5}{18} \times 3.14 \times 12.25
$$
$ 3.14 \times 12.25 = 38.465 $

Now $ \frac{5}{18} \times 38.465 \approx 0.2778 \times 38.465 \approx 10.63 $

✔ Answer: 10.63 m²

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🔹 Problem 6:

- Radius $ r = 8 $ in
- Central angle = $ 270^\circ $

$$
\text{Area} = \frac{270}{360} \times 3.14 \times 8^2 = \frac{3}{4} \times 3.14 \times 64
$$
$ 3.14 \times 64 = 200.96 $

Now $ \frac{3}{4} \times 200.96 = 0.75 \times 200.96 = 150.72 $

✔ Answer: 150.72 in²

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🔹 Problem 7:

- Radius $ r = 12 $ yd
- Central angle = $ 260^\circ $

$$
\text{Area} = \frac{260}{360} \times 3.14 \times 12^2 = \frac{13}{18} \times 3.14 \times 144
$$
$ 3.14 \times 144 = 452.16 $

Now $ \frac{13}{18} \times 452.16 \approx 0.7222 \times 452.16 \approx 326.18 $

✔ Answer: 326.18 yd²

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🔹 Problem 8:

- Radius $ r = 15 $ mm
- Central angle = $ 250^\circ $

$$
\text{Area} = \frac{250}{360} \times 3.14 \times 15^2 = \frac{25}{36} \times 3.14 \times 225
$$
$ 3.14 \times 225 = 706.5 $

Now $ \frac{25}{36} \times 706.5 \approx 0.6944 \times 706.5 \approx 489.94 $

✔ Answer: 489.94 mm²

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✔ Final Answers:

| Problem | Area |
|--------|------|
| 1 | 50.24 cm² |
| 2 | 367.57 ft² |
| 3 | 755.69 cm² |
| 4 | 463.64 ft² |
| 5 | 10.63 m² |
| 6 | 150.72 in² |
| 7 | 326.18 yd² |
| 8 | 489.94 mm² |

Let me know if you'd like this formatted as a printable answer sheet!