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natali 33 [55]
3 years ago
14

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.
Chemistry
1 answer:
Vlad1618 [11]3 years ago
3 0
Answer: 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

Answer: diameter = 8 feet
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