The diameter of the wheels on your car (including the tires) is 25 inches. You are going to drive 218 miles today. Each of your wheels is going to turn by an angle of how many
degrees?
Hint: A mile has 5280 feet, a foot has 12 inches, and the circumference of a circle with a diameter d equals \pi d.
385614
To find the angle in degrees that each wheel turns, we need to determine the distance traveled by a wheel in inches and then convert it to an angle.
First, let's find the circumference of each wheel. The circumference of a circle is equal to π times the diameter. So, the circumference is:
C = π * d = π * 25 inches
Next, we need to find the distance that one wheel will cover in one mile. We know that there are 5280 feet in a mile and 12 inches in a foot. Therefore, the distance in inches covered by one wheel in one mile is:
Distance in inches = 5280 * 12 inches
Now, we can find the number of wheel rotations in one mile by dividing the distance covered in one mile by the circumference of the wheel:
Number of wheel rotations = (Distance in inches) / C
Finally, we need to convert the number of wheel rotations to degrees. We know that a full circle is 360 degrees, so we can find the number of degrees per wheel rotation by:
Degrees per wheel rotation = 360 degrees
Therefore, the angle in degrees that each wheel turns is:
Angle in degrees = Degrees per wheel rotation * (Number of wheel rotations)
Let's calculate it step-by-step.
First, calculate the circumference of the wheel:
C = π * 25 inches
C ≈ 3.1416 * 25 inches
C ≈ 78.54 inches
Next, calculate the distance covered by one wheel in one mile:
Distance in inches = 5280 feet * 12 inches
Distance in inches = 63360 inches
Now, find the number of wheel rotations in one mile:
Number of wheel rotations = Distance in inches / C
Number of wheel rotations ≈ 63360 inches / 78.54 inches
Number of wheel rotations ≈ 806.24 rotations
Lastly, calculate the angle in degrees that each wheel turns:
Degrees per wheel rotation = 360 degrees
Angle in degrees = Degrees per wheel rotation * Number of wheel rotations
Angle in degrees = 360 degrees * 806.24 rotations
Angle in degrees ≈ 290247.04 degrees
Therefore, each of your wheels is going to turn by approximately 290247.04 degrees when you drive 218 miles today.
To find the angle in degrees that each of your wheels will turn, we need to calculate the distance traveled by the car in inches and then convert it to degrees.
First, let's convert the distance traveled from miles to inches. We know that 1 mile is equal to 5280 feet, and 1 foot is equal to 12 inches. So, we can calculate the distance in inches as follows:
Distance in inches = 218 miles * 5280 feet/mile * 12 inches/foot
Now, let's calculate the circumference of the wheel. The circumference of a circle is given by the formula: circumference = π * diameter. Since the diameter of your wheels is given as 25 inches, we can calculate the circumference as:
Circumference of each wheel = π * 25 inches
To find the angle that each wheel turns, we need to divide the distance traveled by the circumference of the wheel:
Angle in degrees = (Distance in inches) / (Circumference of each wheel) * 360 degrees
By substituting the values we calculated, we can find the answer to the question.
The tires will turn
(218*5280*12)/(25π) times
There are 360 degrees per revolution ...