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shannon's living room is a 12 bye 18 foot rectangle. She wants to cover as much of the floor as possible with 6 foot diameter circular rugs without overlap 1). How much of the living room space can shannon cover with the circular rugs to the nearest square foot? ( use PI = 3.14)



Answer :

Solution

We can create the following plot:

Part 1

From this case we can see in the figure that the maxium number of circular rugs are 6

The total area is given by:

A= 12ft * 18 ft= 216 ft2

And the area for a single rug is:

[tex]A=\pi\cdot(3ft)^2=28.274ft^2[/tex]

Then the area for the 6 rugs is:

[tex]A_T=28.274\cdot6=169.646ft^2[/tex]

And rounding to the nearest square foot we got:

170 ft2

Part 2

The remaining space would be given by:

R= 216-170 ft2= 46ft

View image AmesD216515

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