The diameter of the wheels on your car (including the tires) is 25 inches. You are going to drive 305 miles today. Each of your wheels is going to turn by an angle of how many degrees.
I know I'm years late but I'd like to help those who are taking math this year.
In order to solve this problem we need two things, the circumference of the circle and the distance we are driving in relation to our given units (in this case inches)
Circumference can be solved using the formula C=2πr. Doing this we get 78.5394 Inches.
To get the distance traveled we must multiply the number of inches in a mile (63360) by the amount of miles we're traveling (In this case 305) like so: 63360*305= 1.932e+7 Inches (19,320,000)
Next, we want the amount of times the car wheel will revolve. To do this simply divide the circumference by the total distance traveled like so:
19,320,000/78.5394 = 245991.184043
Finally, to solve the amount of degrees of rotation you simply multiply this number by 360° for the amount of degrees in a circle to get your final answer of:
88,556,826.2554°
Well, isn't it wheelie interesting! The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Since we know the diameter of your wheels is 25 inches, the circumference would be 25π inches.
Now, since you're going to drive 305 miles, we need to convert the distance to inches. There are 5,280 feet in a mile, and 12 inches in a foot, so 305 miles is equal to 305 x 5280 x 12 inches. Are you still with me?
Now, to find out how many times your wheels will turn, we divide the total distance traveled in inches by the circumference of one wheel. So the number of times your wheels will turn is (305 x 5280 x 12 inches) ÷ (25π inches).
Now, if I did my math right, your wheels will turn approximately (305 x 5280 x 12) ÷ (25π) times. That's a whole lot of spinning, my friend! Keep your axle-lent sense of humor along the way!
To determine the angle in degrees that each wheel will turn, you first need to know the circumference of the wheel. The circumference is the distance around the circumference of a circle, which can be calculated using the formula:
C = π * d
where C is the circumference and d is the diameter of the wheel. In this case, the diameter is given as 25 inches, so the circumference can be calculated as:
C = π * 25 = 78.5 inches
Next, you need to determine how many times the wheel will turn to cover a distance of 305 miles. Since the circumference of the wheel represents the distance traveled in one complete revolution, you can divide the total distance by the circumference to find out how many revolutions are needed:
Revolutions = Total distance / Circumference
Converting the total distance to inches (since the circumference is in inches), you have:
Total distance = 305 miles * 5280 feet/mile * 12 inches/foot = 18,355,200 inches
Substituting the values, you get:
Revolutions = 18,355,200 inches / 78.5 inches ≈ 233,829.93 revolutions
Since we're looking for the angle in degrees, you can multiply the number of revolutions by 360 degrees per revolution:
Angle in degrees = Revolutions * 360 degrees
Substituting the value, you get:
Angle in degrees = 233,829.93 * 360 ≈ 84,178,376.8 degrees
Therefore, each of your wheels will turn by approximately 84,178,376.8 degrees to cover a distance of 305 miles.
88578151.26
Tire circumference (C) = pi*D = 78.54 inches
Distance travelled (X) = 305*5280*12
1.932*10^7 inches
Number of tire revolutions = X/C = ___
Multiply that by 360 for the number of degrees.