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Exercises for Question Type 3: Calculating the area of sector given a radius and specific angle - IB | RevisionDojo

IB
Question Type 3: Calculating the area of sector given a radius and specific angle

Question Type 3: Calculating the area of sector given a radius and specific angle Exercises

Question 1

Geometry and Trigonometry

Calculate the area of a sector with radius $5$ cm and central angle $\frac{\pi}{3}$ .

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Question 2

A sector of a circle has radius $r$ and angle $\theta$ radians, where $r > 0$ and $0 < \theta < 2\pi$ . The area of the sector is equal to the length of its arc.

Find the value of $r$ .

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Question 3

Given a circle of radius 8 cm, find the combined area of two sectors with angles $\frac{\pi}{6}$ and $\frac{\pi}{3}$ .

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Question 4

Compute the arc length of a sector with radius 10 m and angle $\frac{2\pi}{5}$ .

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Question 5

Mathematics

The area of a sector of a circle is $75\text{ cm}^2$ . If its arc length is $15\text{ cm}$ , find the radius and central angle.

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Question 6

Find the radius of a circle if the arc length of a sector with angle $\frac{\pi}{4}$ is $5\pi\text{ cm}$ .

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Question 7

Given a circle in which a sector’s radius doubles while its central angle stays $\frac{\pi}{3}$ , by what factor does the sector area increase?

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Question 8

A sector has a perimeter (two radii plus arc) of $20 + 4\pi$ cm and a radius of $4$ cm. Find the central angle.

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Question 9

Find the radius of a circle if the area of a sector with central angle $\frac{\pi}{2}$ is 50 cm $^2$ .

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Question 10

Determine the central angle (in radians) of a sector with radius $7\text{ cm}$ and area $28\text{ cm}^2$ .

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Question 11

A sector has an area of $18\pi \text{ cm}^2$ and a radius of $6 \text{ cm}$ . Find its central angle in radians.

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Question 12

The area of a sector is half the area of the circle. Express the central angle in radians.

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