Question

find the circumference and the area of a circle with diameter 10 m. 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 $d = 10$ m, so $r=\frac{d}{2}=\frac{10}{2}=5$ m.

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 $d = 10$ m, we get $C = 10\pi$ m.

Step3: Calculate the area

The formula for the area $A$ of a circle is $A=\pi r^{2}$. Substitute $r = 5$ m into the formula, $A=\pi\times(5)^{2}=25\pi$ m$^{2}$.

Answer:

(a) Circumference: $10\pi$ m
(b) Area: $25\pi$ m$^{2}$