Arc Length Practice
Question 255263 If an arc of 45 degrees on circle A has the same length as an arc of 30
degrees on circle B, find the ratio of the area of circle A to the area of circle B.
Recall:
Problem 71. A circle has a radius of 12 cm. A central angle has measure θ = 3/2 rad.
What is the length of the arc intercepted by the angle?
(a) π/8 cm *(b) 18 cm (c) 8πcm (d) 1/8cm (e) None of these
Solution: (12 cm)(3/2) = 18 cm
Problem 72. A circle has a radius of 10 cm. A central angle has measure θ = 2π/5 rad.
What is the length of the arc intercepted by the angle?
(a) 2π/50 cm (b) 2/25 cm (c) 25/π cm *(d) 4π cm (e) None of these
Solution: (10 cm)(2π/5) = 4π cm
1.1.9 Word problems: arc length and radians
Problem 73. A wheel has a radius of 28 inches. It turns through an angle of 1.2 rad. How
far does a point on the rim travel during the turn? Round your answer to the nearest inch.
(a) 11 in *(b) 34 in (c) 53in (d) 106in (e) None of these
Solution: s = rθ = (28 in)(1.2) = 34 in
trig primer problem set solns Copyright ⃝c Wayne Hacker 2009. All rights reserved. 17
Problem 74. A wheel has a radius of 71 cm. It turns through an angle of 0.6 rad. How far
does a point on the rim travel during the turn? Round your answer to the nearest cm.
(a) 7cm (b) 14cm (c) 27 cm *(d) 43 cm (e) None of these
Solution: s = rθ = (71 cm)(0.6) = 43 cm
Problem 75. A pizza has a radius of 8.2 inches. A slice cut from the pizza has a central
angle of 0.39 rad. What is the length of the crust on the slice? Round your answer to the
nearest 0.1 in.
(a) 0.5 in (b) 1.0 in (c) 2.0 in *(d) 3.2 in (e) None of these
Solution: s = rθ = (8.2 in)(0.39) = 3.2 in
Problem 76. A pie has a radius of 13 cm. A slice cut from the pie has a central angle of
0.29 rad. What is the length of the crust on the slice? Round your answer to the nearest
0.1 cm.
(a) 1.2 cm (b) 2.7 cm *(c) 3.8 cm (d) 4.1 cm (e) None of these
Solution: s = rθ = (13 cm)(0.29) = 3.8 cm
Problem 77. A door measures 34 in from the hinge to the outer edge. It swings through an
angle of 1.4 rad. How far does the outer edge travel? Round your answer to the nearest
inch.
(a) 45 in *(b) 48 in (c) 51in (d) 54in (e) None of these
Solution: s = rθ = (34 in)(1.4) = 48 in
Problem 78. A wheel has a radius of 63 cm. Two adjacent spokes meet at the center at an
angle of 0.51 rad. How long is the rim between the two spokes? Round your answer to
the nearest cm.
*(a) 32 cm (b) 34 cm (c) 36cm (d) 38cm (e) None of these
Solution: s = rθ = (63 cm)(0.51) = 32 cm
trig primer problem set solns Copyright ⃝c Wayne Hacker 2009. All rights reserved. 18
Problem 79. A bicycle wheel has a radius of 27 inches. It turns so that a point on the rim
travels 11 inches. What angle has the wheel turned through? Round your answer to the
nearest 0.01 rad.
(a) 0.31 rad (b) 0.35 rad (c) 0.38 rad *(d) 0.41 rad (e) None of these
Solution: θ = s/r = (11 in)/(27 in) = 0.41 rad
Problem 80. A pizza has a radius of 13 cm. A slice cut from the pizza has 10 cm of crust
on the outside. What is the angle of the slice? Round your answer to the nearest 0.01 rad.
(a) 0.70 rad (b) 0.74 rad *(c) 0.77 rad (d) 0.81 rad (e) None of these
Solution: θ = s/r = (10 cm)/(13 cm) = 0.77 rad