The radius of a circle is 2 cm, what is its curvature?

Options

A. A)1 cm
B. B)4 cm
C. C)0.5 cm
D. D)1.414 cm

Answer

To find the curvature of a circle given its radius, we can follow these steps:

### Step 1: Understand the formula for curvature
The curvature \( K \) of a circle is defined as the reciprocal of its radius \( r \). The formula is:
\[ K = \frac{1}{r} \]

### Step 2: Substitute the given radius into the formula
We are given that the radius \( r \) of the circle is 2 cm. We will substitute this value into the curvature formula:
\[ K = \frac{1}{2 \text{ cm}} \]

### Step 3: Calculate the curvature
Now, we perform the calculation:
\[ K = 0.5 \text{ cm}^{-1} \]

### Step 4: Identify the correct option
From the options provided:
- Option A: 1 cm
- Option B: 4 cm
- Option C: 0.5 cm
- Option D: 1.414 cm

The correct answer is:
\[ \text{Option C: } 0.5 \text{ cm} \]

### Final Answer
The curvature of the circle is \( 0.5 \text{ cm}^{-1} \).

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