1. The problem asks for the volume $V$ of a cylinder in terms of its diameter $d$ and height $h$. 2. The formula for the volume of a cylinder is given by: $$V = \pi r^2 h$$ where $r$ is the radius of the cylinder's base. 3. Since the diameter $d$ is twice the radius, we have: $$r = \frac{d}{2}$$ 4. Substitute $r = \frac{d}{2}$ into the volume formula: $$V = \pi \left(\frac{d}{2}\right)^2 h$$ 5. Simplify the expression inside the parentheses: $$V = \pi \frac{d^2}{4} h$$ 6. Therefore, the formula for the volume of the cylinder in terms of $d$ and $h$ is: $$V = \frac{\pi d^2 h}{4}$$ This formula allows you to calculate the volume if you know the diameter and height of the cylinder.