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# chuck the llama geometry

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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?

tertre  Apr 1, 2018
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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

lynx7  Apr 1, 2018
edited by lynx7  Apr 1, 2018
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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
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If both of them are accurate, why is there a difference of: 22.274 - 21.991 =0.283 m^2 ???!!!.

Guest Apr 1, 2018