Joanna bought three circular rugs to put in her bedroom. Each rug has a 4 ft radius. What is the area of her floor that will be covered by rugs? 

Joanna bought three circular rugs to put in her bedroom. Each rug has a 4 ft radius. What is the area of her floor that will be covered by rugs?

To find the area of the floor covered by the rugs, we need to calculate the total area of the three circular rugs and then subtract it from the total area of Joanna's bedroom floor.

The formula for the area of a circle is: A = πr^2, where r is the radius.

Given that each rug has a radius of 4 ft, the area of one rug is:

A_rug = π × 4^2 square feet.

A_rug = π × 16 square feet.

A_rug = 16π square feet.

Since Joanna bought three identical rugs, the total area covered by the rugs is:

A_total = 3 × 16π square feet.

A_total = 48π square feet.

Now, if we know the dimensions of Joanna's bedroom floor, we can subtract the total area covered by the rugs from the total area of her bedroom floor to find the remaining area. If the dimensions of her bedroom floor are not provided, we can only express the area covered by the rugs as 48π square feet.

Area and Circumference of a Circle

The area A and circumference C of a circle are calculated using the radius r or the diameter d of the circle.

1. Area (A):

   • Formula: A = π * r^2 or A = π * (d^2) / 4

2. Circumference (C):

   • Formula: C = 2 * π * r or C = π * d

In these formulas:

• A represents the area of the circle.
• C represents the circumference of the circle.
• r represents the radius of the circle.
• d represents the diameter of the circle.
• π (pi) is a constant approximately equal to 3.14159.

Here, π (pi) is a constant approximately equal to 3.14159.