Question

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

Explanation:

Step1: Find the radius

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

Step2: Calculate the area

The formula for the area $A$ of a circle is $A=\pi r^{2}$. Substitute $r = 4$ cm into the formula, we get $A=\pi\times(4)^{2}=16\pi$ $cm^{2}$.

Step3: Calculate the circumference

The formula for the circumference $C$ of a circle is $C = 2\pi r$ or $C=\pi d$. Using $d = 8$ cm, we have $C=\pi\times8 = 8\pi$ cm.

Answer:

(a) Area: $16\pi$ $cm^{2}$
(b) Circumference: $8\pi$ cm