Question

find the circumference and the area of a circle with diameter 3 m. use the value 3.14 for π, and do not round your answers. be sure to include the correct units in your answers. circumference: area:

Explanation:

Step1: Find the radius

The radius \( r \) of a circle is half of the diameter \( d \). Given \( d = 3\ m \), so \( r=\frac{d}{2}=\frac{3}{2}\ m \).

Step2: Calculate the circumference

The formula for the circumference \( C \) of a circle is \( C=\pi d \). Substitute \( d = 3\ m \) and \( \pi=3.14 \), we get \( C = 3.14\times3=9.42\ m \).

Step3: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Substitute \( r=\frac{3}{2}\ m \) and \( \pi = 3.14 \). First, \( r^{2}=(\frac{3}{2})^{2}=\frac{9}{4}\ m^{2} \). Then \( A=3.14\times\frac{9}{4}=3.14\times2.25 = 7.065\ m^{2} \).

Answer:

Circumference: \( 9.42\ m \)
Area: \( 7.065\ m^{2} \)