Question

How can Milynn determine the radius of the next circle? Explain your answer.

Answer 1

To determine the radius of the next circle, measure the diameter of the first circle, then take its radius and the half of that radius, Milynn can determine the radius of the circle.

Here are a few ways Milynn can determine the radius of the next circle:

Measure the diameter of the existing circle: If Milynn can measure the distance across the existing circle (the diameter), she can simply divide that measurement by 2 to find the radius.

Use a compass: If Milynn has a compass, she can set the compass to the radius of the existing circle and then use it to draw the next circle. The distance between the compass point and the pencil will be the radius of the new circle.

Use trigonometry: If Milynn knows the circumference of the existing circle, she can use the formula `c = 2πr` (where c is the circumference and r is the radius) to solve for the radius. Once she knows the radius of the existing circle, she can use that to draw the next circle.

Answer 2

Refer to the step-by-step.

Explanation:

To determine the radius of a circle, you need to have some information about the circle. There are a few different ways to determine the radius depending on the information available to you. Here are some common methods...

• Using the circumference of the circle:

The circumference of a circle is the distance around its edge. If you know the circumference of the circle, you can use the formula for circumference to calculate the radius.

`\boxed{\left\begin{array}{ccc}\text{\underline{Circumference of a Circle:}}\\\\C=2\pi r\rightarrow \boxed{r=(C)/(2\pi)} \end{array}\right}`

• Using the area of the circle:

The area of a circle is the measure of the region enclosed by the circle. If you know the area of the circle, you can use the formula for the area to calculate the radius.

`\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Circle:}}\\\\A=\pi r^2\rightarrow \boxed{r=\sqrt{(A)/(\pi) } } \end{array}\right}`

• Using the diameter of the circle:

The diameter of a circle is a straight line passing through the center, and it is equal to twice the radius. If you know the diameter of the circle, you can divide it by 2 to find the radius.

`\boxed{\left\begin{array}{ccc}\text{\underline{Diameter of a Circle:}}\\\\d=2r\rightarrow \boxed{r=(d)/(2) } \end{array}\right}`

• Using coordinate geometry:

If you have the coordinates of the center of the circle and a point on the circle's circumference, you can calculate the distance between them using the distance formula. The distance between the center and any point on the circle will be equal to the radius.

`\boxed{\left\begin{array}{ccc}\text{\underline{The Distance Formula:}}\\\\d=√((x_2-x_1)^2+(y_2-y_1)^2) \end{array}\right}`

Other methods include:

• Using trigonometry
• Using a compass
• Using a laser distance measure
• Using imaging software
• Reference another physical object
• Using grid/graph paper