Question

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

Answer 1

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

$A=(15)(20)=300\ ft^2$

step 2

Find out the area of the circular rug

The area of the circle is

$A=\pi r^{2}$

we have

$\pi =3.14$

$r=6/2=3\ ft$ ----> the radius is half the diameter

substitute

$A=(3.14)(3)^{2}$

$A=28.26\ ft^{2}$

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

$\frac{300}{100\%}=\frac{271.74}{x}\\\\x=100(271.74)/300\\\\x=90.58\%$

Convert to fraction form

$90.58\%=\frac{90.58}{100}$

Simplify

$\frac{4,529}{5,000}$

therefore

There are 271.74 ft^2 not covered by the rug

The percentage not covered by the rug is 90.58%