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

[Guest]

To determine the central angle corresponding to the distance traveled by the hamster on the wheel, we employ the formula for calculating the central angle of a circle given the arc length and radius:

Central Angle (in radians) = Arc Length / Radius

Here, the arc length represents the distance covered by the hamster (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

To convert this angle from radians to degrees, we utilize the conversion factor that 1 radian is roughly 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 degrees

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[Guest]

To find the measure of the central angle, you can use the formula:
Central Angle=Arc Length/Radius
In this case, the arc length is the distance the hamster moved, which is 110cm, and the radius of the hamster wheel is half of its diameter, so it's 48/2=24cm.
Central Angle=10/24
Central Angle≈0.4167radians
Now, to convert radians to degrees, you use the conversion factor 1 radian=180/π degrees:
Central Angle (in degrees)≈0.4167×180/π
°Central Angle (in degrees)≈23.8°
So, the measure of the central angle to the nearest tenth is approximately 23.8°

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