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if the area of a car wheel is 49π sq. inches, how many revolutions does the wheel undergo if the car travels a distance of 112π inches?

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Eduard22sly

The number of revolutions the wheel of the car undergoes is 8 revolutions

Data obtained from the quetion

The following data were obtained from the question:

  • Area of wheel = 49π in²
  • Distance travelled = 112π in
  • Number of revolution =?

How to determine the radius of the wheel

We'll begin by obtaining the radius of the wheel. This can be obtained as follow:

  • Area of wheel (A) = 49π in²
  • Radius of wheel (r) =?

We shall use the area of a circle formula to determine the radius of the wheel.

A = πr²

49π = πr²

Divide both sides by π

r² = 49π / π

r² = 49

r = √49

r = 7 in

How to determine the number of revolutions

  • Distance travelled = 112π in
  • Radius of wheel (r) = 7 in
  • Circumference of wheel = 2πr = 2π × 7 = 14π in
  • Number of revolution =?

The number of revolution made by the wheel can be obtained as follow:

Number of revolution = Distance travelled / circumference

Number of revolution = 112π / 14π

Number of revolution = 8

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