If the radius of circle is 7 cm, then find the perimeter of a quadrant.

Options

A. 25 cm
B. 24 cm
C. 26 cm
D. 27 cm

Answer

To find the perimeter of a quadrant of a circle with a radius of 7 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quadrant**: A quadrant is one-fourth of a circle. The perimeter of a quadrant consists of two parts: the curved part (which is one-fourth of the circumference of the circle) and the two straight sides (which are the radii of the circle).

2. **Calculate the Circumference of the Circle**:
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius. Here, \( r = 7 \) cm.
\[ C = 2 \times \pi \times 7 \]

3. **Substitute the Value of \( \pi \)**:
We can use \( \pi \approx \frac{22}{7} \) for our calculations.
\[ C = 2 \times \frac{22}{7} \times 7 \]

4. **Simplify the Circumference**:
\[ C = 2 \times 22 = 44 \text{ cm} \]

5. **Calculate the Curved Length of the Quadrant**:
Since a quadrant is one-fourth of the circle, the curved length \( L \) of the quadrant is:
\[ L = \frac{1}{4} \times C = \frac{1}{4} \times 44 = 11 \text{ cm} \]

6. **Calculate the Length of the Straight Sides**:
The straight sides of the quadrant are the two radii of the circle. Each radius is 7 cm, so the total length of the straight sides is:
\[ \text{Total straight sides} = 2 \times r = 2 \times 7 = 14 \text{ cm} \]

7. **Calculate the Total Perimeter of the Quadrant**:
Now, we can find the total perimeter \( P \) of the quadrant by adding the curved length and the lengths of the straight sides:
\[ P = L + \text{Total straight sides} = 11 + 14 = 25 \text{ cm} \]

### Final Answer:
The perimeter of the quadrant is **25 cm**.

---