Find the area of the region bounded by the ellipse `(x^2)/(16)+(y^2)/9=1`.

Options

A. `10pi`
B. `11pi`
C. `12pi`
D. `13pi`

Explanation

To find the area of the region bounded by the ellipse given by the equation \(\frac{x^2}{16} + \frac{y^2}{9} = 1\), we can follow these steps:

### Step 1: Identify the parameters of the ellipse
The standard form of the ellipse is given by:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
From the given equation, we can identify:
- \(a^2 = 16\) which gives \(a = 4\)
- \(b^2 = 9\) which gives \(b = 3\)

### Step 2: Use the formula for the area of an ellipse
The area \(A\) of an ellipse is given by the formula:
\[ A = \pi \cdot a \cdot b \]
Substituting the values of \(a\) and \(b\):
\[ A = \pi \cdot 4 \cdot 3 \]

### Step 3: Calculate the area
Now, we can calculate the area:
\[ A = 12\pi \]

### Final Answer
Thus, the area of the region bounded by the ellipse is:
\[ \boxed{12\pi} \]