Question

PLEASE ANSWER ASAP! THANK YOU! SUPER EASY! Mrs. Davis is planning to put a circular rug in her living room. The circumference of the rug is 31.4 ft. Use this information to answer the following questions. Use 3.14 for π. C=πD. A = π r^2.

Answer 1

Part A) The diameter of the rug is
`10\ ft`

Part B) The radius of the rug is
`r=5\ ft`

Part C) The area of the rug is
`78.5\ ft^(2)`

Explanation:

Part A) Find the diameter of the rug

we know that

The circumference of a circle (circular rug) is equal to

`C=\pi D`

where

D is the diameter

we have

`C=31.4\ ft`

`\pi=3.14`

substitute the values and solve for D

`31.4=(3.14)D`

`D=31.4/(3.14)=10\ ft`

Part B) Find the radius of the rug

we know that

The radius of a circle (circular rug) is half the diameter

we have

`D=10\ ft`

`r=D/2`

substitute

`r=10/2=5\ ft`

part C) What is the area the rug is covering?

The area of the circle (circular rug) is equal to

`A=\pi r^(2)`

we have

`r=5\ ft`

`\pi=3.14`

substitute

`A=(3.14)(5)^(2)`

`A=78.5\ ft^(2)`