The formula for the volume of a cylinder is:

$$
\(V=\pi r^2 h\)
$$


We know that $\(h=10 \mathrm{~cm}\)$, but we need to find the length of the radius.
Since the diagonal is 26 cm , we can figure out the diameter using the Pythagorean theorem. The diagonal is the hypotenuse, and the height and diameter are the other two sides.
Let $d=$ length of the diameter:

$$
\(\begin{aligned}
26^2 & =10^2+d^2 \\
676 & =100+d^2 \\
576 & =d^2 \\
d & =24
\end{aligned}\)
$$


So if the diameter is 24 , then the radius will be half of that.

$$
\(r=12\)
$$


Now that we know $\(r=12 \mathrm{~cm}\)$, we can fill in the equation and figure out the volume.

$$
\(V=\pi(12 \mathrm{~cm})^2(10 \mathrm{~cm})=1,440 \pi \mathrm{~cm}^3\)
$$


So any answer choice greater than or equal to $\(1,440 \pi \mathrm{~cm}^3\)$ is correct. $\(1,440 \pi\)$ is approximately 4,524.
This means (A) and (B) are incorrect. (C) is correct because it is exactly the volume of the cylinder, and (D) is correct because $\(4,608= 1,440 \times 3.2\)$, and 3.2 is greater than $\(\pi\)$.