\begin{array}{l}\text{The area enclosed by the curve }\frac{x^2}{16}+\frac{y^2}{25}=1\text{ is:}\end{array}

The correct option is 20π.

Step-by-Step Explanation:

The given equation of the curve is:

$$\frac{x^2}{16}+\frac{y^2}{25}=1$$

This equation represents a standard ellipse centered at the origin (0, 0). The general equation of an ellipse is given by:

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

By comparing the given equation with the standard equation, we can identify the values of $a^2$ and $b^2$:

$$a^2=16\Rightarrow a=4$$

$$b^2=25\Rightarrow b=5$$

Here, a represents the semi-minor axis (since 4 < 5) and b represents the semi-major axis.

The standard formula for the area (A) enclosed by an ellipse is:

$$A=\pi ·a·b$$

Substituting the values of a and b into the formula:

$$A=\pi ·4·5$$

$$A=20\pi$$

Therefore, the area enclosed by the curve is 20π square units.