Question

How is the formula for the circumference of a circle derived? Drag and drop the correct word into each box to complete the explanation.

Answer 1

diameter

circumference

`\pi`

diameter

Explanation:

First, find the length of the diameter (d) and the length of the circumference of the circle (c).

Next, divide the length of the circumference c by the length of the diameter d and set up an equation

`(c)/(d)=\pi`

where the ratio equals to
`\mathbf{\pi }` (the definition of
`\pi`)

Then, solve the equation for the circumference c:

`c=\pi d`

Finally, substitute 2 times the radius for the diameter

`c=\pi \cdot 2r=2\pi r`