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

#1**+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

lynx7
Apr 1, 2018

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

azsun
Apr 1, 2018