Question

area of sectors & arc lengths
for all questions leave your answers to 3 significant figures.
section a
questions 1-6, calculate the area of the sectors.
questions 7 & 8, calculate the radius.
1)
radius: 11 cm, angle: 90 degrees
2)
radius: 8 cm, angle: 47 degrees
3)
radius: 12 cm, angle: 124 degrees
4)
radius: 9 cm, angle: 279 degrees
5)
radius: 16 mm, angle: 311 degrees
6)
radius: 350 m, angle: 209 degrees
7)
area = 60 cm^2, angle: 68 degrees, radius: x
8)
area = 48\pi m^2, angle: 120 degrees (reflex angle), radius: y

Explanation:

Calculate sector areas for Questions 1 to 3

Using the Area of a Sector knowledge point

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$$

Calculate sector areas for Questions 4 to 6

Using the Area of a Sector knowledge point

$$
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$$

Solve for radius in Question 7

We are given the area \(A = 60\text{ cm}^2\) and the angle \(\theta = 68^{\circ}\). We solve for the radius \(x\):

$$ 60 = \frac{68^{\circ}}{360^{\circ}} \times \pi \times x^2 $$

$$ x^2 = \frac{60 \times 360}{68 \times \pi} \approx 101.11 $$

$$ x = \sqrt{101.11} \approx 10.1\text{ cm} $$

Solve for radius in Question 8

We are given the area \(A = 48\pi\text{ m}^2\). The reflex angle for the sector is:

$$ \theta = 360^{\circ} - 120^{\circ} = 240^{\circ} $$

We solve for the radius \(y\):

$$ 48\pi = \frac{240^{\circ}}{360^{\circ}} \times \pi \times y^2 $$

$$ 48 = \frac{2}{3} y^2 $$

$$ y^2 = 72 \implies y = \sqrt{72} \approx 8.49\text{ m} $$

Answer:

No.	Answer
2	\(26.2\text{ cm}^2\)
3	\(156\text{ cm}^2\)
4	\(197\text{ cm}^2\)
5	\(695\text{ mm}^2\)
6	\(223000\text{ m}^2\)
7	\(10.1\text{ cm}\)
8	\(8.49\text{ m}\)