   Chapter 8.1, Problem 47E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Arc Length In Exercises 47-50, use the following information, as shown in the figure. For a circle of radius r, a central angle θ (in radians) intercepts an arc of length s given by s = r θ . Using the Arc Length Formula Complete the table using the formula for arc length. r 8 ft 15 in. 85cm s 12 ft 96 in. 8642 mi θ 1.6 3 π 4 4 2 π 3

To determine

The values of radius r, arc length s and angle θ provided in the table if the length of an arc of a circle of radius r is s=rθ.

r8 ft15 in85 cms12 ft96 in8642 miθ1.63π442π3

Explanation

Given Information:

The length of an arc s of a circle of radius r is s=rθ, where θ is the central angle in radians as provided in the figure.

The provided table is,

r8 ft15 in85 cms12 ft96 in8642 miθ1.63π442π3

Consider the length of arc, s=rθ

From the provided table, the values are r=8 ft and s=12 ft.

Substitute r=8 ft and s=12 ft in the equation s=rθ.

From the provided table, the values are r=15 in and θ=1.6.

Substitute r=15 in and θ=1.6 in the equation s=rθ.

s=(15 in)(1.6)=24 in

From the provided table, the values are r=85 cm and θ=3π4.

Substitute r=85 cm and θ=3π4 in the equation s=rθ.

s=(85 cm)(3π4)=255π4 cm=255×3

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