Question 1

A circular garden has a radius of 10 meters. If a sector of the garden is formed by a central angle of $$\frac{\pi}{3}$$ radians, what is the area of the sector?

Accepted Answer

$$\frac{50\pi}{3}$$

Question 2

A circle has a radius of 8 cm. What is the length of the arc intercepted by a central angle of $$120^{\circ}$$?

Accepted Answer

$$\frac{16\pi}{3}$$

Question 3

A pizza with a radius of 12 inches is cut into a slice with a central angle of $$\frac{\pi}{4}$$ radians. What is the area of the slice?

Accepted Answer

$$18\pi ($$correct)

Question 4

A circular track has a radius of 50 meters. If a runner completes a lap corresponding to a central angle of $$\frac{\pi}{2}$$ radians, what is the length of the arc run?

Accepted Answer

$$25\pi$$

Question 5

A sector of a circle has an area of $$20$$ square meters and a radius of $$5$$ meters. What is the central angle in radians?

Accepted Answer

$$2$$

Question 6

A circular swimming pool has a radius of 15 meters. If a swimmer swims along the edge covering an arc with a central angle of $$60^{\circ}$$, what is the length of the arc?

Accepted Answer

$$5\pi$$

Question 7

A sector of a circle has a radius of $$7 cm $$and a central angle of $$\frac{\pi}{6}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{49\pi}{12}$$

Question 8

A circular field has a radius of $$20$$ meters. What is the length of the arc intercepted by a central angle of $$45^{\circ}$$?

Accepted Answer

$$5\pi$$

Question 9

A sector of a circle has a radius of $$9 cm $$and a central angle of $$\frac{\pi}{2}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{81\pi}{4}$$

Question 10

A circular park has a radius of $$30$$ meters. If a path follows an arc with a central angle of $$\frac{2\pi}{3}$$ radians, what is the length of the path?

Accepted Answer

$$20\pi$$

Question 11

A circular sector has a radius of $$6$$ meters and a central angle of $$150^{\circ}. $$What is the area of the sector?

Accepted Answer

$$15\pi ($$correct)

Question 12

A circular slice of cake has a radius of $$4$$ inches and a central angle of $$\frac{\pi}{3}$$ radians. What is the length of the arc?

Accepted Answer

$$\frac{4\pi}{3}$$

Question 13

A circular fountain has a radius of $$10$$ meters. If the area of a sector is $$25\pi$$ square meters, what is the central angle in radians?

Accepted Answer

$$\frac{1}{1}$$

Question 14

A circular running track has a radius of $$12$$ meters. If a runner covers an arc with a central angle of $$\frac{\pi}{6}$$ radians, what is the length of the arc?

Accepted Answer

$$2\pi ($$correct)

Question 15

A circular sector has a radius of $$5 cm $$and a central angle of $$\frac{\pi}{2}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{25\pi}{4}$$

Question 16

A circular garden has a radius of $$18$$ meters. If a sector has an area of $$54\pi$$ square meters, what is the central angle in radians?

Accepted Answer

$$\frac{1}{3}$$

Question 17

A circular lake has a radius of $$25$$ meters. If a boat travels along an arc with a central angle of $$\frac{\pi}{5}$$ radians, what is the length of the arc?

Accepted Answer

$$5\pi$$

Question 18

A circular pizza has a radius of $$8$$ inches. If a slice has an area of $$8\pi$$ square inches, what is the central angle in radians?

Accepted Answer

$$\frac{1}{2}$$

Question 19

A circular playground has a radius of $$14$$ meters. If a path follows an arc with a central angle of $$\frac{\pi}{7}$$ radians, what is the length of the path?

Accepted Answer

$$\frac{14\pi}{7}$$

Question 20

A circular sector has a radius of $$10 cm $$and a central angle of $$\frac{\pi}{5}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{10\pi}{5}$$

Applications of Radian Measure: Area and Arc Length of a Sector

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