A trophy is a solid cylinder of radius 6 cm and height 15 cm…

Step 1. The bottom. $\pi r^2 = 36\pi\ \text{cm}^2$.

Step 2. The side. $2\pi r h = 2\pi \times 6\ \text{cm} \times 15\ \text{cm} = 180\pi\ \text{cm}^2$.

Step 3. The hollow. The slant height is $l = \sqrt{6^2 + 8^2}\ \text{cm} = 10\ \text{cm}$. The inside surface is $\pi r l = 60\pi\ \text{cm}^2$.

Step 4. The total. $36\pi + 180\pi + 60\pi = 276\pi\ \text{cm}^2$, which is $867.1\ \text{cm}^2$.