To find the area of the circular tray with a diameter of 28 cm, let's go through the calculation step by step.
1. Determine the radius of the tray:
- The radius [tex]\( r \)[/tex] of a circle is half of its diameter.
- Given the diameter is 28 cm, we can calculate the radius as:
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{28}{2} = 14 \text{ cm}
\][/tex]
2. Use the formula for the area of a circle:
- The formula to calculate the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
- Here, [tex]\(\pi\)[/tex] is given as [tex]\(\frac{22}{7}\)[/tex].
3. Calculate the area:
- Substitute the radius [tex]\( r = 14 \text{ cm} \)[/tex] and [tex]\(\pi = \frac{22}{7}\)[/tex] into the formula:
[tex]\[
A = \left(\frac{22}{7}\right) \times (14)^2
\][/tex]
- First, calculate [tex]\(14^2\)[/tex]:
[tex]\[
14^2 = 196
\][/tex]
- Now multiply by [tex]\(\frac{22}{7}\)[/tex]:
[tex]\[
A = \left(\frac{22}{7}\right) \times 196
\][/tex]
- Simplify the multiplication:
[tex]\[
A = \frac{22 \times 196}{7} = \frac{4312}{7} = 616 \text{ cm}^2
\][/tex]
Thus, the area of the tray is:
[tex]\[
\boxed{616 \text{ cm}^2}
\][/tex]
