×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide

Solved: Grazing goat problems. Consider the following

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 48E Chapter 10.3

Calculus: Early Transcendentals | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

4 5 1 248 Reviews
29
4
Problem 48E

Grazing goat problems. Consider the following sequence of problems related to grazing goats tied to a rope. (See The Guided Projects for more grazing goat problems.)

A circular concrete slab of unit radius is surrounded by grass. A goat is tied to the edge of the slab with a rope of length 0 ≤ a ≤ 2 (see figure). What is the area of the grassy region that the goat can graze? Note that the rope can extend over the concrete slab. Check your answer with the special cases a = 0 and a = 2.

Step-by-Step Solution:

Solution 48E

Step 1:

A circular concrete slab of unit radius is surrounded by grass. A goat is tied to the edge of the slab with a rope of length 0 ≤ a ≤ 2 (see figure). What is the area of the grassy region that the goat can graze? Note that the rope can extend over the concrete slab. Check your answer with the special cases a = 0 and a = 2.

Step 2:

This can be drawn as

To find the area of the grassy region that the goat can graze

Step 3:

We have to find the area of the shaded region .

Let us consider the distance

Therefore by pythagoras theorem we get

Now lets us consider the triangle RPQ and RQP

Let us take   and

Thus we get

And  

Step 4:

Now to find the area of the shaded region we will have to add the area of the segments S1 and S2.

Area of a segment can be found by adding the triangle and the sector.

Therefore area of the shaded region is

Step 5 of 7

Chapter 10.3, Problem 48E is Solved
Step 6 of 7

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Solved: Grazing goat problems. Consider the following

×
Log in to StudySoup
Get Full Access to Calculus - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Calculus - Textbook Survival Guide
×
Reset your password