Emily went to a local shop to purchase some round rugs. each rug has a radius of 3 feet. she is trying to cover as much of the floor of her 18 foot by 20 foot living room as possible without any overlap of the rugs. how much of the bare floor will be visible around the rugs? a. 20.76 square feet b. 254.47 square feet c. 9 square feet d. 105.5 square feet

D. 105.5 square feet

Step-by-step explanation:

Given:

The  rug has a radius of 3 feet.

The floor dimensions are 18 feet by 20 feet.

Now we have to find the area of the rug using area of the circle formula and also we need to find the area of the floor which is in rectangle shape.

Area of a circle =

r = 3 feet and the value of

Now plug in the given values in the above formula, we get

Area of a rug = 3.14*3*3

Area of a each rug is  28.27 square feet.

Now let's find the area of the floor.

Area of the floor = length * width

Here length = 18 feet and width = 20

The area of the floor = 18*20

= 360 square feet

Now we have to find how many rugs needed to cover the floor without overlap.

Here the radius of the rug = 3 feet

The diameter of the rug = 2*radius = 2*3 = 6 feet

So one rug covers 6 feet by length and width.

Therefore, 18/6 = 3

The width is 20 feet

20/6 = 3, we have to take the whole number part only.

So Emily needs only 3*3 = 9 rugs.

The area of the 9 rugs = 9*28.27  = 254.43

To find the bare floor will be visible around the rugs, we need to subtract the area of the 9 rugs from the floor area

Bare floor = 360 - 254.43

Bare floor = 105.5 square feet.