A wheel rolls 140cm while rotating 210 degrees. What is the circumference of the wheel??
use a ratio,
C/360 = 140/210
C = 360(140/210)
= ...
Find all values of theta in radians over th set of real numbers given the equation.
2sinthetacostheta=sintheta
To find the circumference of the wheel, we can use the formula:
Circumference = Distance / Angle
Given that the wheel rolls 140 cm and rotates 210 degrees, we can substitute these values into the formula:
Circumference = 140 cm / 210 degrees
Since the units of distance and angle are different, we need to convert them to the same unit. Let's convert degrees to radians, as it is the standard unit for measuring angles.
To convert degrees to radians, we use the formula:
Radians = Degrees * (π / 180)
Substituting the given angle of 210 degrees into the formula, we get:
Radians = 210 degrees * (π / 180)
Simplifying this expression, we get:
Radians = 21/2 * π
Now, let's go back to the formula for the circumference:
Circumference = 140 cm / (21/2 * π)
To simplify this expression, we can divide 140 by 21/2:
Circumference = (140 cm * 2/21) / π
Calculating the numerator, we get:
Numerator = 140 cm * 2/21 = 280/21 cm
Therefore, the circumference of the wheel is:
Circumference = (280/21 cm) / π
This is the exact value of the circumference. If you require a numerical approximation, you can substitute the value of π as 3.14159 and perform the division to get the approximate value.
To find the circumference of the wheel, you need to know the relationship between the distance it rolls and the rotation it completes.
The distance traveled by a wheel in one complete rotation is equal to its circumference. So, if we can determine the distance the wheel travels in 210 degrees, we can find its circumference.
To calculate the distance traveled in 210 degrees, we can use the proportion:
Distance traveled in 210 degrees / 360 degrees = Distance traveled in one complete rotation / Circumference of the wheel
Let's calculate it step by step:
1. Set up the proportion:
Distance traveled in 210 degrees / 360 degrees = Distance traveled in one complete rotation / Circumference of the wheel
2. Substitute the given values:
Distance traveled in 210 degrees / 360 degrees = 140cm (as given) / Circumference of the wheel
3. Solve for the unknown, which is the circumference of the wheel:
Distance traveled in 210 degrees = (140cm * 360 degrees) / 210 degrees
4. Calculate the distance traveled in 210 degrees:
Distance traveled in 210 degrees = (14,400 cm degrees) / 210 degrees
Distance traveled in 210 degrees ≈ 68.57 cm
Thus, the distance traveled in 210 degrees is approximately 68.57 cm.
Therefore, the circumference of the wheel is approximately 68.57 cm.