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An arc of circle M has length 32 centimeters and the corresponding central angle has a radian measure of . What is the radius of the circle?
The radius of the circle is
centimeters.

Verified Answer :

GinnyAnswer

To determine the radius of the circle, we can use the formula relating the arc length, the central angle in radians, and the radius. The formula is given by:

\(\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \]\)

We are given:
- Arc Length = 32 centimeters
- Central Angle = 1 radian

We need to solve for the radius (r). Rearrange the formula to isolate the radius:

\(\[ \text{Radius} = \frac{\text{Arc Length}}{\text{Central Angle}} \]\)

Substitute the given values into the formula:

\(\[ \text{Radius} = \frac{32 \text{ centimeters}}{1 \text{ radian}} \]\)

\(\[ \text{Radius} = 32 \text{ centimeters} \]\)

Thus, the radius of the circle is 32 centimeters.

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