A 15ftX20ft room has a 6ft diameter circular rug in it. How much of the flood is not covered by the rug?

Answer:There are 271.74 ft^2 not covered by the rugThe percentage not covered by the rug is 90.58%Step-by-step explanation:step 1Find out the area of the roomThe area of the rectangular room is[tex]A=(15)(20)=300\ ft^2[/tex]step 2Find out the area of the circular rugThe area of the circle is[tex]A=\pi r^{2}[/tex]we have[tex]\pi =3.14[/tex][tex]r=6/2=3\ ft[/tex] ----> the radius is half the diametersubstitute[tex]A=(3.14)(3)^{2}[/tex][tex]A=28.26\ ft^{2}[/tex]step 3Find out what percentage of the room is not covered by the rugwe know that300 ft^2 represent the 100%sousing proportionFind out what percentage represent the difference (300-28.26)=271.74 ft^2Letx ----> the percentage not covered by the rug[tex]\frac{300}{100\%}=\frac{271.74}{x}\\\\x=100(271.74)/300\\\\x=90.58\%[/tex]Convert to fraction form[tex]90.58\%=\frac{90.58}{100}[/tex]Simplify[tex]\frac{4,529}{5,000}[/tex]thereforeThere are 271.74 ft^2 not covered by the rugThe percentage not covered by the rug is 90.58%