Volume of Inscribed Cylinder in Prism

Imagine a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 3 cm. Within this prism, a right circular cylinder is inscribed, where the height of the cylinder is equal to the height of the prism and the base radius of the cylinder is half the width of the prism. You are asked to calculate the volume of the cylinder.

Recall that the volume $V$ of a cylinder can be calculated using the formula:

$V = heta r^2 h$,

where $r$ is the radius of the base and $h$ is the height of the cylinder.