Question

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

Step2: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Substitute \( \pi = 3.14 \) and \( r = 4 \) yd:
\( A=3.14\times4^{2}=3.14\times16 = 50.24 \) square yards.

Step3: Calculate the circumference

The formula for the circumference \( C \) of a circle is \( C=\pi d \) (or \( C = 2\pi r \)). Substitute \( \pi=3.14 \) and \( d = 8 \) yd:
\( C = 3.14\times8=25.12 \) yards.

Answer:

Area: \( 50.24 \) square yards
Circumference: \( 25.12 \) yards