Question

find the circumference and the area of a circle with diameter 8 km. write your answers in terms of π, and be sure to include the correct units in your answers. (a) circumference: (b) area:

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter $d$. Given $d = 8$ km, so $r=\frac{d}{2}=\frac{8}{2}=4$ km.

Step2: Calculate the circumference

The formula for the circumference $C$ of a circle is $C = 2\pi r$ or $C=\pi d$. Using $C=\pi d$ with $d = 8$ km, we get $C = 8\pi$ km.

Step3: Calculate the area

The formula for the area $A$ of a circle is $A=\pi r^{2}$. Substituting $r = 4$ km, we have $A=\pi\times(4)^{2}=16\pi$ km².

Answer:

(a) Circumference: $8\pi$ km
(b) Area: $16\pi$ km²