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


1. 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.

2. 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.

3. 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.

4. 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.

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Circumference of a circle - derivation

This page describes how to derive the formula for the circumference of a circle.

Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as

π

=

c

d

Rearranging this to solve for c we get

c

=

π

d

The diameter of a circle is twice its radius, so substituting 2r for d

c

=

2

π

r

If you know the area

Recall that the area of a circle is given by

area

=

π

r

2

Solving this for r

r

2

=

a

π

So

r

=

√

a

π

The circumference c of a circle is

c

=

2

π

r

MrRoyal

The explanation that can be used to calculate the circumference of a circle is: (d)  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.

To determine the circumference of a circle, we start by dividing the circumference (C) by the diameter (d) of the circle.

So, we have:

[tex]\frac Cd[/tex]

This quotient equals [tex]\pi[/tex].

So, we have:

[tex]\frac Cd = \pi[/tex]

Multiply both sides by d

[tex]C = \pi d[/tex]

The relationship between the diameter (d) and radius (r) is:

[tex]d = 2r[/tex]

So, we have:

[tex]C = \pi (2r)[/tex]

Multiply

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

The above step is represented by option (d)

Read more about circumference at:

https://brainly.com/question/2633255

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