A tire has a diameter of 3ft. ow many times will it rotate in order to roll across a field that is 297 yd long? Round answer to the nearest tenth if necessary
5 years ago
Answered By Kiley C
In order to solve this question you will need to use the formula for the circumference of a circle (since a tire is circular). This is 2*pi*r or pi*d - where d is your diameter and r is your radius.
We are given our diameter = 3ft, however the total distance is in yards so, divide the total distance by 3, since that is the conversion from yd to feet (297/3).
Therefore you get the formula
99 = x*(pi*3) where x is the number of times the tire has rolled because you have to go around the full circumference of a tire to roll it once.
99/3 = x*pi
33 = x*pi
33/pi = x
x = 10.54
5 years ago
Answered By Megan R
diameter = 3 ft
Circumference = pi*d = 9.4247 ft
1 ft = 0.3333 yard so
9.4247 ft / 3 = 3.1416 yards = Circumference
297 yards / 3.1416 yards = 94.538 or 94.5 rotations, rounded to the nearest tenth.
5 years ago
Answered By Steven G
Circumference of the tire = ?x d
Circumference of the tire = 3.14 × 3 feet
Circumference of the tire = 9.42
Now, you have to convert the field measurement from yards to feet, so 297 yards x 3 = 891 feet
The field is 891 feet, and the tire is 9.42 feet around (circumference). To get the answer to how many rotations it takes the tire to go from one end of the field to another, you divide 9.42 feet into 891 feet. So....
891 ? 9.42 = 94.59 or 94.6 rotations
5 years ago
Answered By Jackie C
A:
The total distance L=297 yards=297 yards*(3 feet/yard)=891 feet
One roattion of the tire equals a distance of l=pai*D=3pai, where D is the diameter of the tire in feet.
Therefore, the number of rotations is n=L/l=891/(3pai)=891/(3*3.1415926535897932...)=94.5.
This solution is under the condition that the axe of the tire touches the starting point of the 297 yards disctane.
5 years ago
Answered By Suman G
In order to calculate the number of rolls, we need to calculate the circumference of the tire by the following formula:
$Circumfarence=2\pi r=\pi d$Circumƒarence=2πr=πd , where r is the radius of the tire and d is the diameter.
In our case r= diameter/2 = 3 ft/2 = 1.5 ft
Hence, Circumfarence = 2*3.14*1.5 ft = 9.42 ft.
So, each rotation of tire will cover 9.42 ft.
Total distance to cover = 297 yd = 297 * 3 ft = 891 ft (Conversion, 1yd = 3 ft)
Hence, number of rotation will be calculated from the following formula:
Total number of rotation = (total distance to cover)/(distance covered in each rotation) = 891 ft/9.42 ft = 94.6 rotations.
Hence, 94.6 rotation of the tire is needed to roll across the field that is 297 yd long.
5 years ago
Answered By Kiley C
In order to solve this question you will need to use the formula for the circumference of a circle (since a tire is circular). This is 2*pi*r or pi*d - where d is your diameter and r is your radius.
We are given our diameter = 3ft, however the total distance is in yards so, divide the total distance by 3, since that is the conversion from yd to feet (297/3).
Therefore you get the formula
99 = x*(pi*3) where x is the number of times the tire has rolled because you have to go around the full circumference of a tire to roll it once.
99/3 = x*pi
33 = x*pi
33/pi = x
x = 10.54
5 years ago
Answered By Megan R
diameter = 3 ft
Circumference = pi*d = 9.4247 ft
1 ft = 0.3333 yard so
9.4247 ft / 3 = 3.1416 yards = Circumference
297 yards / 3.1416 yards = 94.538 or 94.5 rotations, rounded to the nearest tenth.
5 years ago
Answered By Steven G
Circumference of the tire = ?x d
Circumference of the tire = 3.14 × 3 feet
Circumference of the tire = 9.42
Now, you have to convert the field measurement from yards to feet, so 297 yards x 3 = 891 feet
The field is 891 feet, and the tire is 9.42 feet around (circumference). To get the answer to how many rotations it takes the tire to go from one end of the field to another, you divide 9.42 feet into 891 feet. So....
891 ? 9.42 = 94.59 or 94.6 rotations
5 years ago
Answered By Jackie C
A:
The total distance L=297 yards=297 yards*(3 feet/yard)=891 feet
One roattion of the tire equals a distance of l=pai*D=3pai, where D is the diameter of the tire in feet.
Therefore, the number of rotations is n=L/l=891/(3pai)=891/(3*3.1415926535897932...)=94.5.
This solution is under the condition that the axe of the tire touches the starting point of the 297 yards disctane.
5 years ago
Answered By Suman G
In order to calculate the number of rolls, we need to calculate the circumference of the tire by the following formula:
$Circumfarence=2\pi r=\pi d$Circumƒ arence=2πr=πd , where r is the radius of the tire and d is the diameter.
In our case r= diameter/2 = 3 ft/2 = 1.5 ft
Hence, Circumfarence = 2*3.14*1.5 ft = 9.42 ft.
So, each rotation of tire will cover 9.42 ft.
Total distance to cover = 297 yd = 297 * 3 ft = 891 ft (Conversion, 1yd = 3 ft)
Hence, number of rotation will be calculated from the following formula:
Total number of rotation = (total distance to cover)/(distance covered in each rotation) = 891 ft/9.42 ft = 94.6 rotations.
Hence, 94.6 rotation of the tire is needed to roll across the field that is 297 yd long.