Question

find the circumference and the area of a circle with diameter 5 yd. use the value 3.14 for π, and do not round your answers. be sure to include the correct units in your answers.

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter $d$. Given $d = 5$ yd, so $r=\frac{d}{2}=\frac{5}{2}$ yd.

Step2: Calculate the circumference

The formula for the circumference $C$ of a circle is $C = 2\pi r$ or $C=\pi d$. Using $d = 5$ yd and $\pi=3.14$, we have $C = 3.14\times5=15.7$ yd.

Step3: Calculate the area

The formula for the area $A$ of a circle is $A=\pi r^{2}$. Substitute $r = \frac{5}{2}$ yd and $\pi = 3.14$ into the formula: $A=3.14\times(\frac{5}{2})^{2}=3.14\times\frac{25}{4}=19.625$ yd².

Answer:

Circumference: $15.7$ yd
Area: $19.625$ yd²