Exercises for Question Type 4: Applying both arc length and area of sector in solving equations - IB | RevisionDojo

IB
Question Type 4: Applying both arc length and area of sector in solving equations

Question Type 4: Applying both arc length and area of sector in solving equations Exercises

Question 1

A sector has area $12\pi$ and subtends an arc of length $6\pi$ . Determine the radius of the circle and the measure of the central angle in degrees.

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Question 2

A quarter circle has an arc length of $8\pi$ . Find the radius of the circle and the area of the quarter circle.

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Question 3

A sector's arc length is one quarter of the circle's circumference and its area is $9\pi$ . Find the circle's radius.

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Question 4

A sector has area $18\pi$ and central angle $\frac{3\pi}{4}$ radians. Find the radius of the circle.

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Question 5

A sector with central angle $\frac{\pi}{2}$ has its area numerically equal to its arc length.

Find the radius and the common numerical value.

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Question 6

A sector has arc length $9$ and area $18$ . Find the radius of the circle and the central angle in radians.

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Question 7

A sector with central angle $\tfrac{2\pi}{3}$ radians has an arc length of $10\pi$ . Find the radius of the circle and the area of the sector.

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Question 8

A sector has central angle $150^\circ$ and an arc length of $5\pi$ cm. Find its radius and area.

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Question 9

A sector with central angle $\frac{\pi}{3}$ has its area equal to three times its arc length. Find the radius of the circle.

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Question 10

A full circle is partitioned into a sector that has one-sixth of the circumference as its arc and an area of $20\pi$ . Find the circle's radius.

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Question 11

A sector has area $8\pi$ and arc length $4\pi$ . Find the radius of the circle and the measure of its central angle in radians.

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Question 12

A sector has an arc length of $15$ and an area of $30$ . Find the radius of the circle and the measure of the central angle in radians.

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