For this case we have that by definition, the area of a circle is given by:
![A = \pi r ^ 2](https://img.qammunity.org/2020/formulas/mathematics/high-school/ndf6spelq6ca1w6cpmtw1slb3g67pphw4h.png)
Where,
We have then that the radio is given by:
![r = \frac {d} {2}](https://img.qammunity.org/2020/formulas/mathematics/high-school/kqcs0przrb2vd6n62weyhlnln9w4e5irb7.png)
Where,
- d: diameter of the circle
Substituting values we have:
![r = \frac {18} {2}\\r = 9](https://img.qammunity.org/2020/formulas/mathematics/high-school/z41m2mcj5ipse0t9hh2gwp6gmsqiui31wv.png)
Then, calculating the area we have:
![A = \pi (9) ^ 2\\A = 81 \pi](https://img.qammunity.org/2020/formulas/mathematics/high-school/xg3srdmyweb1cb6btve2w3qe8sc2c388ag.png)
Answer:
on a circular serving tray that has a diameter of 18 in can be placed:
![A = 81 \pi](https://img.qammunity.org/2020/formulas/mathematics/high-school/1r60co1pwgxx055vfck4joq9dpql1w12ra.png)