A string is wound is tightly around a wheel. When the end of the string is pulled through a distance of 10 cm, the wheel rotates through 5 revolutions. What is the radius of the wheel?
5*2*pi*R = 10*pi*R = 10 cm
Solve for R
.318
0.00318
To find the radius of the wheel, we can first find the circumference of the wheel using the information given.
The distance the end of the string is pulled through, which is 10 cm, represents the length of string wound around the wheel. This length is equal to the circumference of the wheel after 5 complete revolutions, which is equal to 5 times the circumference of the wheel.
Therefore, we can set up the equation:
10 cm = 5 * (2 * π * r),
where r is the radius of the wheel.
To find the radius, we rearrange the equation:
r = 10 cm / (5 * 2 * π) = 10 cm / (10 * π) = 1 cm / π.
Thus, the radius of the wheel is approximately 0.3183 cm, or 0.32 cm rounded to two decimal places.