A capsule is a cylinder with a hemisphere at each end…

Step 1. The cylinder part. $h = 15\ \text{mm} - 2 \times 2.5\ \text{mm} = 10\ \text{mm}$.

Step 2. Its volume. $\pi r^2 h = \pi \times 6.25\ \text{mm}^2 \times 10\ \text{mm} = 62.5\pi\ \text{mm}^3$.

Step 3. The two ends. $\dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi \times 15.625\ \text{mm}^3 = \dfrac{62.5\pi}{3}\ \text{mm}^3$.

Step 4. The total. $62.5\pi + \dfrac{62.5\pi}{3} = \dfrac{250\pi}{3}\ \text{mm}^3$, which is $261.8\ \text{mm}^3$.