Question

which of these represents the volume of a cylinder of diameter d and length l?
(a) $pi d^{2}l$
(b) $pi dl$
(c) $\frac{pi d^{2}l}{4}$
(d) $d^{2}l$

Explanation:

Step1: Recall volume formula for cylinder

The volume formula of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height (or length in this case).

Step2: Express radius in terms of diameter

Given diameter $D$, the radius $r=\frac{D}{2}$.

Step3: Substitute radius into volume formula

Substitute $r = \frac{D}{2}$ and $h = L$ into $V=\pi r^{2}h$. We get $V=\pi(\frac{D}{2})^{2}L=\frac{\pi D^{2}L}{4}$.

Answer:

C. $\frac{\pi D^{2}L}{4}$