the radius of the tires of a car is 13 inches, and they are revolving at the rate of 506 revolutions per minute. how fast is the car traveling in miles per hour.
A. 6.23pi mph
B. 1.25pi mph
C. 149.50pi mph
D. 12.46pi mph
you had a similar question the other day.
one rotation would cover 26pi inches.
so in one minute it would cover 506(26pi) inches, or 60(506)26pi inches per hour.
Now how many inches in a mile?
(geesh, I hate this non-metric nonsense)
1 mile = 5280x12 inches
so his rate would be 60(506)26pi/(5280*12) mph
= 39.1 mph which is the same as 12.46pi or answer D
ok thanks alot
To find how fast the car is traveling in miles per hour, we need to find the circumference of the tires, and multiply it by the number of revolutions per minute to get the distance traveled in inches per minute. Then, we can convert inches per minute to miles per hour.
1. Finding the circumference:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Given that the radius of the tires is 13 inches, the circumference can be calculated as follows:
C = 2π(13)
C ≈ 2 * 3.14 * 13
C ≈ 81.64 inches
2. Calculating the distance traveled in inches per minute:
Since the tires are revolving at the rate of 506 revolutions per minute, we can multiply the circumference by the number of revolutions to get the distance traveled in inches per minute:
Distance = 81.64 inches/rev * 506 rev/min
Distance ≈ 41254.64 inches/min
3. Converting inches per minute to miles per hour:
To convert inches per minute to miles per hour, we need to find the number of inches in a mile and the number of minutes in an hour.
There are 12 inches in a foot, and 5280 feet in a mile.
Therefore, there are 12 * 5280 = 63360 inches in a mile.
There are 60 minutes in an hour.
So, to find the distance traveled in miles per hour, we divide the distance in inches per minute by the number of inches in a mile and multiply by the number of minutes in an hour:
Distance (miles/hour) = (Distance (inches/min) * 60) / 63360
Distance (miles/hour) ≈ (41254.64 * 60) / 63360 ≈ 39.08625 miles/hour
Therefore, the car is traveling at a speed of approximately 39.08625 miles per hour.
Since the answer choices are provided in terms of "pi," we can also express the speed as:
39.08625 ≈ 12.46π
So, the correct answer is option D: 12.46π mph.
To find the speed of the car in miles per hour, we need to use the formula:
Speed = circumference × number of revolutions × time
First, we need to find the circumference of the tire. The circumference of a circle is calculated using the formula:
Circumference = 2πr
where r is the radius. Given that the radius of the tire is 13 inches, the circumference is:
Circumference = 2 × π × 13 inches
Next, we need to convert the inches to miles. There are 12 inches in a foot, and 5280 feet in a mile:
1 mile = 5280 feet
1 foot = 12 inches
So, using the conversion factor, we can convert the circumference from inches to miles:
Circumference (in miles) = (Circumference (in inches)) / (12 inches/foot) / (5280 feet/mile)
Now we can calculate the speed by multiplying the circumference by the number of revolutions per minute and dividing by the number of minutes in an hour:
Speed (in miles per hour) = (Circumference (in miles)) × (number of revolutions per minute) × (60 minutes/hour)
Finally, we substitute the given values into the formula and calculate the answer:
Circumference (in inches) = 2 × π × 13 = 26π inches
Circumference (in miles) = (26π inches) / (12 inches/foot) / (5280 feet/mile) = 26π / (12 × 5280) miles
Speed (in miles per hour) = (26π / (12 × 5280)) × (506) × (60) = (26π / 6336) × 506 × 60 = (26π / 6336 × 506 × 60) mph
Calculating this expression gives us an approximate value of 6.23π mph.
Therefore, the answer is A. 6.23π mph.