Q42. - Algebra 1

Question

Find the circumference and area of each circle. Round to nearest tenth. 

Step-by-Step Solution

Answer

$\begin{array}{l}\text{Circumference of given circle }C=50.3\text{ cm}\\ \text{Area of given circle }A=201.1{\text{ cm}}^2\end{array}$

Step 1. Calculate the radius of the given circle.

In the given circle, observe that the diameter of the circle is 16 cm, so the radius must be half of the diameter, that is,

$\begin{array}{l}r=\frac{d}{2}\\ r=\frac{16}{2}\\ r=8\text{ cm}\end{array}$

Step 2. Formula used.

The circumference and area of a circle of radius r are given by.

$\begin{array}{l}\text{Circumference of a circle }C=2\pi r\\ \text{Area of a circle }A=\pi r^2\end{array}$

Step 3. Calculate the circumference of the given circle.

In order to find the circumference of the circle, use the above formula and substitute 8 for r and simplify further as shown below.

$\begin{array}{l}\text{Circumference of circle}\\ C=2\pi \left(8\right)\\ C=16\pi \\ C=50.3\text{ cm}\end{array}$

Step 4. Calculate the area of the given circle.

In order to find the area of the circle, use the above formula and substitute 8 for r and simplify further as shown below:

$\begin{array}{l}\text{Area of circle }\\ A=\pi r^2\\ A=\pi {\left(8\right)}^2\\ A=64\pi \\ A=201.1{\text{ cm}}^2\end{array}$

Therefore,

$\begin{array}{l}\text{Circumference of given circle }C=50.3\text{ cm}\\ \text{Area of given circle }A=201.1{\text{ cm}}^2\end{array}$