Question

arc length/sector area worksheet
period: _______
part 1: area of a sector
find the area of the shaded sector. use 3.14 for $pi$.
1.
area = ________
2.
area = ________
3.
area = ________
4.
area = ________
part 2: arc length
find the length of the indicated arc. use 3.14 for $pi$.
5.
length of the arc de = ________
6.
length of the arc lm = ________
7.
length of the arc xy = ________
8.
length of the arc ab = ________

Explanation:

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Part 1: Area of a Sector

Problem 1

Step1: Recall sector area formula

Area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta=130^\circ$, $r=11\ \text{cm}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{130^\circ}{360^\circ} \times 3.14 \times 11^2 = \frac{13}{36} \times 3.14 \times 121 \approx 138.99\ \text{cm}^2$

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Problem 2

Step1: Recall sector area formula

Area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta=310^\circ$, $r=11\ \text{in}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{310^\circ}{360^\circ} \times 3.14 \times 11^2 = \frac{31}{36} \times 3.14 \times 121 \approx 324.91\ \text{in}^2$

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Problem 3

Step1: Recall sector area formula

Area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta=270^\circ$, $r=9\ \text{ft}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{270^\circ}{360^\circ} \times 3.14 \times 9^2 = \frac{3}{4} \times 3.14 \times 81 = 190.755\ \text{ft}^2$

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Problem 4

Step1: Recall sector area formula

Area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta=40^\circ$, $r=14\ \text{cm}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{40^\circ}{360^\circ} \times 3.14 \times 14^2 = \frac{1}{9} \times 3.14 \times 196 \approx 68.42\ \text{cm}^2$

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Part 2: Arc Length

Problem 5

Step1: Recall arc length formula

Length = $\frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=160^\circ$, $r=8\ \text{m}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{160^\circ}{360^\circ} \times 2 \times 3.14 \times 8 = \frac{4}{9} \times 50.24 \approx 22.33\ \text{m}$

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Problem 6

Step1: Recall arc length formula

Length = $\frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=50^\circ$, $r=5\ \text{ft}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{50^\circ}{360^\circ} \times 2 \times 3.14 \times 5 = \frac{5}{36} \times 31.4 \approx 4.36\ \text{ft}$

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Problem 7

Step1: Recall arc length formula

Length = $\frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=90^\circ$, $r=10\ \text{m}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{90^\circ}{360^\circ} \times 2 \times 3.14 \times 10 = \frac{1}{4} \times 62.8 = 15.7\ \text{m}$

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Problem 8

Step1: Recall arc length formula

Length = $\frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=200^\circ$, $r=5\ \text{m}$, $\pi=3.14$

Step2: Substitute values and calculate

$\frac{200^\circ}{360^\circ} \times 2 \times 3.14 \times 5 = \frac{5}{9} \times 31.4 \approx 17.44\ \text{m}$

Answer:

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Part 1: Area of a Sector

1. $138.99\ \text{cm}^2$
2. $324.91\ \text{in}^2$
3. $190.755\ \text{ft}^2$
4. $68.42\ \text{cm}^2$

Part 2: Arc Length

1. $22.33\ \text{m}$
2. $4.36\ \text{ft}$
3. $15.7\ \text{m}$
4. $17.44\ \text{m}$