Hamster wheel

[Guest]

A scientist is collecting distance and angle measurement data from a hamster moving inside a hamster wheel. A hamster moves a distance of 10 cm from a position P to position Q. If the diameter of the hamster wheel is 48 cm. Find the measure between 0° and 360° of the central angle (between 0° and 360°) to the nearest tenth.

[Guest]

To find the central angle corresponding to the distance the hamster has moved, we can use the formula for calculating the central angle of a circle given the arc length and the radius:

Central Angle (in radians) = Arc Length / Radius

In this case, the arc length is the distance the hamster moved (10 cm), and the radius of the hamster wheel is half of its diameter (48 cm / 2 = 24 cm).

Central Angle (in radians) = 10 cm / 24 cm = 5/12 radians

Now, to convert the angle from radians to degrees, we use the fact that 1 radian is approximately equal to 57.2958 degrees.

Central Angle (in degrees) = Central Angle (in radians) * (180 / π)
Central Angle (in degrees) ≈ (5/12) * (180 / π) ≈ 75.522 degree