I'll mark the best or the first as brainliest.

Answer:
Here the error is
[tex]\pi {r}^{2} [/tex]
It should have been ,
[tex]2\pi {r}^{2} [/tex]
Step-by-step explanation:
Corrected formula:
[tex]2\pi {r}^{2} + 2\pi rh[/tex]
[tex] = 2\pi ({5}^{2}) + 2\pi(5)(10.6)[/tex]
[tex] = 50\pi + 106\pi[/tex]
[tex] = 156\pi[/tex]
[tex] = 489.84 {yd}^{2} [/tex]
[tex]approx . \: 489.8 {yd}^{2} (ans)[/tex]