Which of the following degree measures is equivalent to `2.25pi` radians ?

Options

A. `101.25^@`
B. `202.5^@`
C. `405^@`
D. `810^@`

Answer

To convert \(2.25\pi\) radians to degrees, we can follow these steps:

### Step 1: Understand the conversion factor
We know that:
\[ \pi \text{ radians} = 180 \text{ degrees} \]

### Step 2: Set up the conversion
To convert \(2.25\pi\) radians to degrees, we can multiply \(2.25\pi\) by the conversion factor \(\frac{180 \text{ degrees}}{\pi \text{ radians}}\):
\[ 2.25\pi \text{ radians} \times \frac{180 \text{ degrees}}{\pi \text{ radians}} \]

### Step 3: Simplify the expression
The \(\pi\) in the numerator and denominator cancels out:
\[ 2.25 \times 180 \text{ degrees} \]

### Step 4: Calculate the multiplication
Now, we calculate \(2.25 \times 180\):
\[ 2.25 \times 180 = 405 \text{ degrees} \]

### Step 5: Conclusion
Thus, \(2.25\pi\) radians is equivalent to \(405\) degrees.

The correct option is **Option 3: 405 degrees**.

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