Chapter 11, Problem 40RP

To determine

To calculate:Thegrazing area for horse G.

Answer to Problem 40RP

Thegrazing area for horse G is $113\pi m^2$ .

Explanation of Solution

Given information:

The rope is 12 m.

The barn is 8 m by 10 m.

Formula used:

Area of a circle: $A=\pi r^2$

r = radius of circle.

Calculation:

  

G has $\frac{3}{4}$ of a 12 m radius circle, plus $\frac{1}{4}$ of both a 2 m radius circle and 4 m radius circle.

Area of 12 m radius circle $=\frac{3}{4}\pi r^2=\frac{3}{4}\pi {\left(12\right)}^2=\frac{3}{4}144\pi =108\pi m^2$

Area of 2 m radius circle $=\frac{1}{4}\pi r^2=\frac{1}{4}\pi {\left(2\right)}^2=\frac{1}{4}4\pi =\pi m^2$

Area of 4 m radius circle $=\frac{1}{4}\pi r^2=\frac{1}{4}\pi {\left(4\right)}^2=\frac{1}{4}16\pi =4\pi m^2$

Grazing Area $=108\pi +\pi +4\pi =113\pi m^2$

Since the barn is a rectangle, it forms right angles and takes up $\frac{1}{4}$ of each circle formed.