If the diameter of a monster truck tire is 3.5 m and it makes one rotation every 5 seconds, how far does the tire
roll in 1 minute?
Diameter 3.5
radius: 3.5/2 = 1.75
12(2pi x 1.75)
=131.9 m
the book states that its 263.89 m?
What did I do wrong?
Looks good to me. Book must be in error.
the book is wrong you're right they didn't find the radius they used the diameter as their radius that is why your answer seem to differ from theirs but you're actually right.
Well, it seems like there was a little mix-up in your calculations. First of all, to find the circumference of the tire, you need to use the equation:
Circumference = 2 * pi * radius
So in this case, it would be:
Circumference = 2 * 3.14 * 1.75 = 10.99 meters
Now, to find the distance the tire rolls in 1 minute, we need to figure out how many times it rotates in that time. Since the tire makes one rotation every 5 seconds, in 1 minute (which is 60 seconds), it will rotate:
60 seconds / 5 seconds = 12 times
So, to find the total distance rolled, we multiply the circumference of the tire by the number of rotations:
12 rotations * 10.99 meters = 131.88 meters
Therefore, the tire should roll approximately 131.88 meters in 1 minute, not 263.89 meters as stated in the book. Perhaps the book made a typo or a clownish error.
To find the distance the tire rolls in one minute, we first need to calculate the circumference of the tire.
The circumference of a circle can be calculated using the formula: circumference = 2πr, where r is the radius of the circle.
In this case, the radius is half of the diameter, so it is 1.75 m.
The circumference is:
circumference = 2π(1.75) = 3.5π m
Now, since the tire makes one rotation every 5 seconds, we need to find out how many rotations it will make in one minute (60 seconds).
Number of rotations in one minute = 60 seconds / 5 seconds = 12 rotations
To find the distance the tire rolls in one minute, we multiply the circumference by the number of rotations.
Distance rolled in one minute = 3.5π m * 12 rotations = 42π m
Using the approximation of π as 3.14, we can calculate the approximate distance rolled in one minute:
Distance rolled in one minute ≈ 42 * 3.14 ≈ 131.88 m
From my calculations, the tire should roll approximately 131.88 meters in one minute. This is close to the value you have calculated.
It seems that the book answer of 263.89 m is incorrect.
To calculate the distance the tire rolls in 1 minute, you first need to find the circumference of the tire, which is the distance covered in one full rotation. The formula for circumference is C = 2πr, where r is the radius of the tire.
From the given information, you correctly identified the radius as 3.5/2 = 1.75 m. Plugging this value into the circumference formula, we have:
C = 2π * 1.75
C ≈ 11.0 m
Therefore, the tire rolls approximately 11.0 meters in one rotation.
Next, to find the distance the tire rolls in 1 minute, you need to determine the number of rotations it makes in that time. Since the tire makes one rotation every 5 seconds, we can calculate the number of rotations in 1 minute:
1 minute = 60 seconds
Number of rotations in 1 minute = (60 seconds) / (5 seconds/rotation)
Number of rotations in 1 minute = 60 / 5
Number of rotations in 1 minute = 12 rotations
Finally, to find the total distance the tire rolls in 1 minute, you multiply the distance covered in one rotation by the number of rotations:
Total distance = (distance per rotation) * (number of rotations)
Total distance = 11.0 m * 12
Total distance = 132.0 m
Based on these calculations, the tire should roll approximately 132.0 meters in 1 minute. It seems that the book's answer of 263.89 meters is incorrect. Double-checking your calculations, it appears that you made the correct calculations and arrived at the correct answer.