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Chuck the llama is tied to the corner of a \(2\text{ m}\)  by \(3\text{ m}\) shed on a \(3\text{ m}\) leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed?

 

 Apr 1, 2018
 #1
avatar+557 
+2

area of rectangle=length*width

area of rectangle=3*2

area of rectangle=6m^2

 

area of circle=π*r^2

area of circle=π*3^2

area of circle=π*9

area of circle=28.27433388m^2

 

area of circle - area of rectangle= area around the outside of the shed

28.27433388m^2-6m^2=22.27433388m^2

 

 

winkwinkwink

 Apr 1, 2018
edited by lynx7  Apr 1, 2018
 #2
avatar+175 
+3

Chuck can play in the three quarters of the circle with radius 3 that does not have any area inside the shed.

The area of that is \(\frac {3}{4} \times9 \pi = \frac{27\pi} {4}\).

One meter of Chuck's rope can extend below the shed on the bottom right corner with one meter left. So, Chuck has a quarter circle with radius \(1\) he can play in.

The total is \(\frac{27\pi} {4} + \frac{\pi}{4}= \frac{28\pi}{4} = \boxed{7\pi}\) .

 Apr 1, 2018
edited by azsun  Apr 1, 2018
 #3
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If both of them are accurate, why is there a difference of: 22.274 - 21.991 =0.283 m^2 ???!!!.

 Apr 1, 2018

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