Question

find the circumference and the area of a circle with diameter 6 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 \( d = 6\) yd, so \( r=\frac{d}{2}=\frac{6}{2}=3\) yd.

Step2: Calculate the circumference

The formula for the circumference \( C \) of a circle is \( C = \pi d\) (or \(C = 2\pi r\)). Using \(d = 6\) yd and \(\pi=3.14\), we have \(C=3.14\times6 = 18.84\) yd.

Step3: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2}\). Substituting \(r = 3\) yd and \(\pi = 3.14\), we get \(A=3.14\times3^{2}=3.14\times9 = 28.26\) \(yd^{2}\).

Answer:

Circumference: \(18.84\) yd
Area: \(28.26\) \(yd^{2}\)