In a circle with radius 7 cm, the length of a minor arc is always less than ......... cm.

Options

A. 11
B. 22
C. 15
D. `pi`

Answer

To find the maximum length of a minor arc in a circle with a radius of 7 cm, we can use the formula for the length of an arc. The length \( L \) of an arc is given by the formula:

\[ L = r \theta \]

where:
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

### Step 1: Identify the maximum angle for a minor arc
A minor arc is defined as an arc that is less than half of the circle. The angle corresponding to half of the circle is \( \pi \) radians. Therefore, for a minor arc, the maximum angle \( \theta \) can be:

\[ \theta < \pi \text{ radians} \]

### Step 2: Substitute the values into the arc length formula
We know the radius \( r = 7 \) cm. We can substitute this value into the arc length formula:

\[ L < r \theta \]
\[ L < 7 \theta \]

### Step 3: Substitute the maximum angle for the minor arc
Now, substituting the maximum angle \( \theta = \pi \):

\[ L < 7 \times \pi \]

### Step 4: Calculate the numerical value
Using the approximation \( \pi \approx \frac{22}{7} \):

\[ L < 7 \times \frac{22}{7} \]
\[ L < 22 \text{ cm} \]

### Conclusion
Thus, the length of a minor arc in a circle with a radius of 7 cm is always less than **22 cm**.

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