Question

find the circumference and the area of a circle with diameter 8 m. 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 its diameter \( d \). Given \( d = 8 \, \text{m} \), so \( r=\frac{d}{2}=\frac{8}{2} = 4 \, \text{m} \).

Step2: Calculate the circumference

The formula for the circumference \( C \) of a circle is \( C=\pi d \) (or \( C = 2\pi r \)). Using \( \pi = 3.14 \) and \( d = 8 \, \text{m} \), we have \( C=3.14\times8=25.12 \, \text{m} \).

Step3: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). We know \( r = 4 \, \text{m} \) and \( \pi=3.14 \), so \( A = 3.14\times4^{2}=3.14\times16 = 50.24 \, \text{m}^2 \).

Answer:

Circumference: \( 25.12 \, \text{m} \)
Area: \( 50.24 \, \text{m}^2 \)