Which explanation can be used to derive the formula for the circumference of a circle?

A. Find the length of the radius. Then find the circumference. Use the square of the radius to set up an equation showing the relationship that the square of the radius equals the π times circumference. Then rearrange the equation to equal the circumference.

B. Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to π . Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.

C. Find the length of the diameter and double this amount. Subtract it from the length of the circumference. Set an equation to show the difference equaling the ratio between a circumference and radius. Then rearrange the equation to solve for the circumference.

D. Find the length of the radius and the area of the circle. Divide the area by the radius to get a quotient of π . Write an equation showing the area of a circle equals this quotient times the radius. Then substitute the area for 3 times the circumference and rearrange the equation to equal the circumference.

First, find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately π times. Use this relationship to writing an equation showing the ratio of circumference to diameter equaling π. Then rearrange the equation to solve for the circumference. Substitute the diameter for 2 times the radius

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Lanuel Lanuel · Answer 2 · 2021-11-08T14:35:06+01:00

The explanation which can be used to derive the formula for the circumference of a circle is: B. Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to π . Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.

Mathematically, the circumference of a circle is given by the formula:

[tex]Circumference = 2 \pi r[/tex]

Where:

r is the radius of a circle.

The steps involved in deriving the the formula for the circumference of a circle are:

1. You should determine the diameter's length (D) and circumference's length (C) respectively.

2. You should divide the circumference's length (C) by the length of the diameter (D): [tex]\frac{C}{D}[/tex]

3. You should set up an equation to show that the ratio of the circumference to the diameter is equal to [tex]\pi[/tex]: [tex]C:D = C:\pi D=\frac{C}{D} = \pi[/tex]

4. Then, you should rearrange the equation by solving it for the circumference: [tex]C =\pi D[/tex]

5. Lastly, you should substitute two (2) times the radius for the diameter: [tex]C = \pi (2r) = 2\pi r[/tex]

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