Convert 11 radian into degree.

Options

A. 600
B. 630
C. 660
D. 700

Explanation

To convert 11 radians into degrees, we can follow these steps:

### Step 1: Understand the conversion factor
We know that:
\[ \pi \text{ radians} = 180 \text{ degrees} \]
From this, we can find the conversion factor from radians to degrees:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

### Step 2: Set up the conversion for 11 radians
To convert 11 radians into degrees, we multiply 11 by the conversion factor:
\[ 11 \text{ radians} = 11 \times \frac{180}{\pi} \text{ degrees} \]

### Step 3: Substitute the value of \(\pi\)
Using the approximation \(\pi \approx \frac{22}{7}\), we can substitute this value into our equation:
\[ 11 \text{ radians} = 11 \times \frac{180}{\frac{22}{7}} \text{ degrees} \]

### Step 4: Simplify the expression
To simplify the expression, we can multiply by the reciprocal of \(\frac{22}{7}\):
\[ = 11 \times 180 \times \frac{7}{22} \]

### Step 5: Calculate the multiplication
Now, we perform the multiplication:
\[ = \frac{11 \times 180 \times 7}{22} \]
Calculating \(11 \times 180\):
\[ 11 \times 180 = 1980 \]
Now, substituting back:
\[ = \frac{1980 \times 7}{22} \]

### Step 6: Simplify the fraction
Now, we simplify \(\frac{1980}{22}\):
\[ 1980 \div 22 = 90 \]
Thus, we have:
\[ = 90 \times 7 = 630 \]

### Final Result
Therefore, \(11\) radians is equal to \(630\) degrees.

### Summary
\[ 11 \text{ radians} = 630 \text{ degrees} \]

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