The diameter is an important parameter of a circumference. Geometrically, the diameter is defined as a secant line to the circumference that passes through its center. Another important parameter is the radius of the circumference; that is defined as the segment drawn from the center to a point on the perimeter of the circumference. Between the radius r and the diameter d the following relationship is established:
r = d/2
So if the diameter d1 of a circumference increases twice, the new diameter is d2 = 2d1, then we can establish the following relationship:
d2 = 2d1 r1 = d1/2 r2 = d2/2 = 2d1/2
r2/r1 = (2d1/2)/(d1/2)
r2/r1 = 2
r2 = 2r1
If the diameter increases twice, then the radius also increases twice.
Let the diameter be `d` and radius `r`
The relationship between d and r is `d = 2r ` or `r = 1/2 d`
If we double the diameter, then
so, `2*d = 2* 2r`
`2d = 4r`
That means if we double the diameter radius also will get doubled.
Lets check this with an example
Suppose diameter is 10 cm, then the radius is half of it, i.e, 5 cm.
Now double the diameter, it becomes 20 cm, then the radius becomes half of it 10 cm. This is twice of the original radius.
`d_1 = 20 cm =gt r_1 = 1/2 20 = 10 cm = 2r`
If diameter is doubled then the radius will be?
I will solve this using examples.
Suppose the original diameter is 2. Then the original radius must be 1.
If we double the original diameter, 4, then the radius would be 2.
The relationship formula between diameter and radius is:
If we double the diameter, 2D, the radius will also double to 4D.
2D = 4R
This tells us that if we doubled the original diameter, the radius would also be doubled. The new radius will end up being the same as the original diameter.
typo: radius will also double to 4R****
When I have questions like this, I like to think about it with a few examples. In this case let's use the following example:
If `d=4` then `r=2`
But if we double the diameter:
then the radius should be:
Which is twice as long as it was at the beginning. So if the diameter of a circle is doubled, then so is the radius of a circle. Since both are doubling this is known as a direct relationship, as opposed to an inverse relationship.