Question

what is the circumference of a circle with a diameter of 4 km? what is the area?

Explanation:

Step1: Recall circle formulas

The formula for the circumference \( C \) of a circle is \( C = \pi d \) (where \( d \) is the diameter) or \( C = 2\pi r \) (where \( r \) is the radius). The formula for the area \( A \) of a circle is \( A=\pi r^{2} \), and the radius \( r=\frac{d}{2} \). Given \( d = 4\space km \), first find the radius: \( r=\frac{4}{2}=2\space km \).

Step2: Calculate the circumference

Using \( C=\pi d \), substitute \( d = 4 \): \( C=\pi\times4 = 4\pi\space km \) (or approximately \( 4\times3.14 = 12.56\space km \)).

Step3: Calculate the area

Using \( A = \pi r^{2} \), substitute \( r = 2 \): \( A=\pi\times(2)^{2}=\pi\times4 = 4\pi\space km^{2} \) (or approximately \( 4\times3.14 = 12.56\space km^{2} \)).

Answer:

Circumference: \( 4\pi\space km \) (or \( 12.56\space km \)); Area: \( 4\pi\space km^{2} \) (or \( 12.56\space km^{2} \))