Jose’ has a circular rug on the floor of his bedroom. if the area of the rug is 16π square feet, what is the diameter of the rug? the diameter of the rug is feet.

8 feet

Explanation:

1) The diameter and the area of a circle are related by this formula:

Area = π (radius)^2 = π (diameter / 2) ^2 = π (diameter)^2 / 4

2) Since you know the area you can find the formula for the diameter:

(diameter)^2 = 4 * area / π

=> diamter = √ [4*area / π]

3) Replace the value of the area

area = 16π (feet)^2

=> diameter = √ [ 4 * 16 π (feet)^2 / π ] = √ 64 feet = 8 feet

diameter = 8 feet