Your bedroom is in the shape of a square that is 14 feet long on each side. will a circular rug with a circumference of 50.24 feet fit in your room? if not, by how many feet is the rug too wide?

We need to find the diameter of the rug and compare it to the side length of the room — which is given.

The formula for the circumference of a circle is below — where represents the circumference and represents the diameter.

Plug in the value we know.

Replace with its approximate value — .

Divide both sides of the equation by .

The diameter of the rug is feet, which means it will not fit into the room. It is 2 feet too wide ().

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a