Question 1

Find the length of the arc $s$ subtended by a central angle $\theta=108^{\circ} 29^{\prime}$ of a circle of radius $r=1.73 \mathrm{~cm}$.

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Question 2

Find the radius $r$ of a circle where a central angle $\theta=123^{\circ} 45^{\prime}$ subtends an arc length $s=9.02 \mathrm{ft}$.

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Question 3

Find the central angle $\theta$ of a circle of radius $r=4.000 \mathrm{~m}$ that subtends a length of arc $s=0.391 \mathrm{~m}$.

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Question 4

Find the central angle $\theta$ of a circle of radius $r=7.500 \mathrm{~m}$ that subtends a length of arc $s=0.755 \mathrm{~m}$.

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Question 5

Find the central angle $\theta$ of a circle of radius $r=43.5 \mathrm{~cm}$ that subtends a length of arc $s=154 \mathrm{~mm}$.

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Question 6

What arc length is subtended by a central angle of $76.5^{\circ}$ in a circle of radius $1.27 \mathrm{~m}$ ?

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Question 7

What arc length is subtended by a central angle of $108.2^{\circ}$ in a circle of radius $21.2 \mathrm{~cm}$ ?

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Question 8

What arc length is subtended by a central angle of $4 \pi / 9$ in a circle of radius $145 \mathrm{~m}$ ?

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Question 9

The hour hand of a clock is $7.18 \mathrm{~cm}$ long. How far does the tip of the hand travel between 2 P.M. and 9 P.M.?

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Question 10

Determine the latitude of a city that is 1944 miles from the equator. Assume that the earth is a sphere with radius 3960 miles.

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Question 11

A $12.2 \mathrm{~m}$ long pendulum swings $4.80^{\circ}$ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

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Question 12

An isosceles triangle is to be inscribed in a circle of radius $8.00 \mathrm{~cm}$. Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length $11.34 \mathrm{~cm}$.

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Question 13

A circular highway curve has a radius of $100 \mathrm{~m}$ and a central angle of $15^{\circ} 45^{\prime} 30^{\prime \prime}$ (measured to the centre line of the road). What is the length of the curve?

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Question 14

Calculate the area of a sector with radius $12.5 \mathrm{~cm}$ and arc length of $7.24 \mathrm{~cm}$.

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Question 15

A certain town is at a latitude of $24.9^{\circ} \mathrm{S}$. How far is it from the North Pole? Assume that the earth is a sphere with radius $6370 \mathrm{~km}$.

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Question 16

Determine the latitude of a city that is $165 \mathrm{~km}$ from the equator. Assume that the earth is a sphere with radius $6370 \mathrm{~km}$.

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Question 17

Fill in the missing values.

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 ...

Question 18

Fill in the missing values.

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 ...

Question 19

Fill in the missing values.

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 ...

Question 20

Calculate the angular velocity in revolutions per minute of a wheel that rotates at $83 \overline{0}$ radians per second.

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Quiz 16: Radian Measure, Arc Length, and Circular Motion

Find the length of the arc $s$ subtended by a central angle $\theta=108^{\circ} 29^{\prime}$ of a circle of radius $r=1.73 \mathrm{~cm}$ .

Find the radius $r$ of a circle where a central angle $\theta=123^{\circ} 45^{\prime}$ subtends an arc length $s=9.02 \mathrm{ft}$ .

Find the central angle $\theta$ of a circle of radius $r=4.000 \mathrm{~m}$ that subtends a length of arc $s=0.391 \mathrm{~m}$ .

Find the central angle $\theta$ of a circle of radius $r=7.500 \mathrm{~m}$ that subtends a length of arc $s=0.755 \mathrm{~m}$ .

Find the central angle $\theta$ of a circle of radius $r=43.5 \mathrm{~cm}$ that subtends a length of arc $s=154 \mathrm{~mm}$ .

What arc length is subtended by a central angle of $76.5^{\circ}$ in a circle of radius $1.27 \mathrm{~m}$ ?

What arc length is subtended by a central angle of $108.2^{\circ}$ in a circle of radius $21.2 \mathrm{~cm}$ ?

What arc length is subtended by a central angle of $4 \pi / 9$ in a circle of radius $145 \mathrm{~m}$ ?

The hour hand of a clock is $7.18 \mathrm{~cm}$ long. How far does the tip of the hand travel between 2 P.M. and 9 P.M.?

Determine the latitude of a city that is 1944 miles from the equator. Assume that the earth is a sphere with radius 3960 miles.

A $12.2 \mathrm{~m}$ long pendulum swings $4.80^{\circ}$ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

An isosceles triangle is to be inscribed in a circle of radius $8.00 \mathrm{~cm}$ . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length $11.34 \mathrm{~cm}$ .

A circular highway curve has a radius of $100 \mathrm{~m}$ and a central angle of $15^{\circ} 45^{\prime} 30^{\prime \prime}$ (measured to the centre line of the road). What is the length of the curve?

Calculate the area of a sector with radius $12.5 \mathrm{~cm}$ and arc length of $7.24 \mathrm{~cm}$ .

A certain town is at a latitude of $24.9^{\circ} \mathrm{S}$ . How far is it from the North Pole? Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Determine the latitude of a city that is $165 \mathrm{~km}$ from the equator. Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Fill in the missing values.

Fill in the missing values.

Fill in the missing values.

Calculate the angular velocity in revolutions per minute of a wheel that rotates at $83 \overline{0}$ radians per second.

Quiz 16: Radian Measure, Arc Length, and Circular Motion

Find the length of the arc sss subtended by a central angle θ=108∘29′\theta=108^{\circ} 29^{\prime}θ=108∘29′ of a circle of radius r=1.73 cmr=1.73 \mathrm{~cm}r=1.73 cm .

Find the radius rrr of a circle where a central angle θ=123∘45′\theta=123^{\circ} 45^{\prime}θ=123∘45′ subtends an arc length s=9.02fts=9.02 \mathrm{ft}s=9.02ft .

Find the central angle θ\thetaθ of a circle of radius r=4.000 mr=4.000 \mathrm{~m}r=4.000 m that subtends a length of arc s=0.391 ms=0.391 \mathrm{~m}s=0.391 m .

Find the central angle θ\thetaθ of a circle of radius r=7.500 mr=7.500 \mathrm{~m}r=7.500 m that subtends a length of arc s=0.755 ms=0.755 \mathrm{~m}s=0.755 m .

Find the central angle θ\thetaθ of a circle of radius r=43.5 cmr=43.5 \mathrm{~cm}r=43.5 cm that subtends a length of arc s=154 mms=154 \mathrm{~mm}s=154 mm .

What arc length is subtended by a central angle of 76.5∘76.5^{\circ}76.5∘ in a circle of radius 1.27 m1.27 \mathrm{~m}1.27 m ?

What arc length is subtended by a central angle of 108.2∘108.2^{\circ}108.2∘ in a circle of radius 21.2 cm21.2 \mathrm{~cm}21.2 cm ?

What arc length is subtended by a central angle of 4π/94 \pi / 94π/9 in a circle of radius 145 m145 \mathrm{~m}145 m ?

The hour hand of a clock is 7.18 cm7.18 \mathrm{~cm}7.18 cm long. How far does the tip of the hand travel between 2 P.M. and 9 P.M.?

Determine the latitude of a city that is 1944 miles from the equator. Assume that the earth is a sphere with radius 3960 miles.

A 12.2 m12.2 \mathrm{~m}12.2 m long pendulum swings 4.80∘4.80^{\circ}4.80∘ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

An isosceles triangle is to be inscribed in a circle of radius 8.00 cm8.00 \mathrm{~cm}8.00 cm . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length 11.34 cm11.34 \mathrm{~cm}11.34 cm .

A circular highway curve has a radius of 100 m100 \mathrm{~m}100 m and a central angle of 15∘45′30′′15^{\circ} 45^{\prime} 30^{\prime \prime}15∘45′30′′ (measured to the centre line of the road). What is the length of the curve?

Calculate the area of a sector with radius 12.5 cm12.5 \mathrm{~cm}12.5 cm and arc length of 7.24 cm7.24 \mathrm{~cm}7.24 cm .

A certain town is at a latitude of 24.9∘S24.9^{\circ} \mathrm{S}24.9∘S . How far is it from the North Pole? Assume that the earth is a sphere with radius 6370 km6370 \mathrm{~km}6370 km .

Determine the latitude of a city that is 165 km165 \mathrm{~km}165 km from the equator. Assume that the earth is a sphere with radius 6370 km6370 \mathrm{~km}6370 km .

Fill in the missing values.

Fill in the missing values.

Fill in the missing values.

Calculate the angular velocity in revolutions per minute of a wheel that rotates at 830‾83 \overline{0}830 radians per second.

Find the length of the arc $s$ subtended by a central angle $\theta=108^{\circ} 29^{\prime}$ of a circle of radius $r=1.73 \mathrm{~cm}$ .

Find the radius $r$ of a circle where a central angle $\theta=123^{\circ} 45^{\prime}$ subtends an arc length $s=9.02 \mathrm{ft}$ .

Find the central angle $\theta$ of a circle of radius $r=4.000 \mathrm{~m}$ that subtends a length of arc $s=0.391 \mathrm{~m}$ .

Find the central angle $\theta$ of a circle of radius $r=7.500 \mathrm{~m}$ that subtends a length of arc $s=0.755 \mathrm{~m}$ .

Find the central angle $\theta$ of a circle of radius $r=43.5 \mathrm{~cm}$ that subtends a length of arc $s=154 \mathrm{~mm}$ .

What arc length is subtended by a central angle of $76.5^{\circ}$ in a circle of radius $1.27 \mathrm{~m}$ ?

What arc length is subtended by a central angle of $108.2^{\circ}$ in a circle of radius $21.2 \mathrm{~cm}$ ?

What arc length is subtended by a central angle of $4 \pi / 9$ in a circle of radius $145 \mathrm{~m}$ ?

The hour hand of a clock is $7.18 \mathrm{~cm}$ long. How far does the tip of the hand travel between 2 P.M. and 9 P.M.?

A $12.2 \mathrm{~m}$ long pendulum swings $4.80^{\circ}$ on each side of the vertical. Determine the length of the arc travelled by the end of the pendulum.

An isosceles triangle is to be inscribed in a circle of radius $8.00 \mathrm{~cm}$ . Determine the angles of the triangle to degrees, minutes, and seconds if its base subtends an arc of length $11.34 \mathrm{~cm}$ .

A circular highway curve has a radius of $100 \mathrm{~m}$ and a central angle of $15^{\circ} 45^{\prime} 30^{\prime \prime}$ (measured to the centre line of the road). What is the length of the curve?

Calculate the area of a sector with radius $12.5 \mathrm{~cm}$ and arc length of $7.24 \mathrm{~cm}$ .

A certain town is at a latitude of $24.9^{\circ} \mathrm{S}$ . How far is it from the North Pole? Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Determine the latitude of a city that is $165 \mathrm{~km}$ from the equator. Assume that the earth is a sphere with radius $6370 \mathrm{~km}$ .

Calculate the angular velocity in revolutions per minute of a wheel that rotates at $83 \overline{0}$ radians per second.