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?


tertre  Apr 1, 2018

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





lynx7  Apr 1, 2018
edited by lynx7  Apr 1, 2018

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

azsun  Apr 1, 2018
edited by azsun  Apr 1, 2018

If both of them are accurate, why is there a difference of: 22.274 - 21.991 =0.283 m^2 ???!!!.

Guest Apr 1, 2018

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