Answer:
There are 271.74 ft^2 not covered by the rug
The percentage not covered by the rug is 90.58%
Step-by-step explanation:
step 1
Find out the area of the room
The area of the rectangular room is
[tex]A=(15)(20)=300\ ft^2[/tex]
step 2
Find out the area of the circular rug
The 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 diameter
substitute
[tex]A=(3.14)(3)^{2}[/tex]
[tex]A=28.26\ ft^{2}[/tex]
step 3
Find out what percentage of the room is not covered by the rug
we know that
300 ft^2 represent the 100%
so
using proportion
Find out what percentage represent the difference (300-28.26)=271.74 ft^2
Let
x ----> 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]
therefore
There are 271.74 ft^2 not covered by the rug
The percentage not covered by the rug is 90.58%
