Volume of Inscribed Cylinder in a Prism

Consider a rectangular prism with dimensions 12 cm, 8 cm, and 5 cm. Inside this prism, a right circular cylinder is inscribed that touches the sides of the prism. The height of the cylinder is equal to the height of the prism. Determine the volume of the cylinder in cubic centimeters.

Recall that the volume $V$ of a cylinder is given by the formula:

$$V = ext{Base Area} imes ext{Height}$$

The base area of a cylinder can be calculated using the formula:

$$ ext{Base Area} =\frac{1}{2} imes ext{Diameter}^2 imes\frac{orall}{4}$$.