If the perimeter of a quadrant is 42 cm, then find the radius of quadrant.

Options

A. 11.76 cm
B. 12.30 cm
C. 12.8 cm
D. 11 cm

Answer

To find the radius of the quadrant given that its perimeter is 42 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Perimeter of a Quadrant**:
The perimeter \( P \) of a quadrant is given by the formula:
\[ P = \frac{1}{4} \times 2\pi r + 2r \]
This simplifies to:
\[ P = \frac{\pi r}{2} + 2r \]

2. **Set Up the Equation**:
We know the perimeter is 42 cm, so we can set up the equation:
\[ 42 = \frac{\pi r}{2} + 2r \]

3. **Combine Like Terms**:
To simplify the equation, we can multiply everything by 2 to eliminate the fraction:
\[ 84 = \pi r + 4r \]

4. **Factor Out \( r \)**:
Now, we can factor \( r \) out of the right side:
\[ 84 = r(\pi + 4) \]

5. **Solve for \( r \)**:
To find \( r \), divide both sides by \( \pi + 4 \):
\[ r = \frac{84}{\pi + 4} \]

6. **Substitute the Value of \( \pi \)**:
Using \( \pi \approx 3.14 \):
\[ r = \frac{84}{3.14 + 4} = \frac{84}{7.14} \]

7. **Calculate the Value of \( r \)**:
Now, perform the division:
\[ r \approx \frac{84}{7.14} \approx 11.76 \text{ cm} \]

### Final Answer:
The radius of the quadrant is approximately \( 11.76 \) cm.

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