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

There are 271.74 ft^2 not covered by the rug

The percentage not covered by the rug is 90.58%

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

`(300)/(100\%)=(271.74)/(x)\\\\x=100(271.74)/300\\\\x=90.58\%`

Convert to fraction form

`90.58\%=(90.58)/(100)`

Simplify

`(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%