Question

the high school soccer field is decorated with the logo of the schools soccer team in a circular design. the center of the design is placed in the middle of the field. the edge of the design is 9\frac{3}{4} yards from its center. a.) what is the circumference of the design? b.) what is the area of the design?

Explanation:

Step1: Identify the radius

The distance from the center to the edge of the circular - design is the radius $r$. Given $r = 9\frac{3}{4}=\frac{9\times4 + 3}{4}=\frac{39}{4}$ yards.

Step2: Calculate the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r=\frac{39}{4}$ into the formula: $C = 2\pi\times\frac{39}{4}=\frac{39\pi}{2}\approx\frac{39\times3.14}{2}=61.23$ yards.

Step3: Calculate the area

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r = \frac{39}{4}$ into the formula: $A=\pi\times(\frac{39}{4})^{2}=\pi\times\frac{1521}{16}\approx\frac{3.14\times1521}{16}=297.70125$ square - yards.

Answer:

a. The circumference of the design is $\frac{39\pi}{2}\approx61.23$ yards.
b. The area of the design is $\frac{1521\pi}{16}\approx297.70$ square yards.