Question

As diameter of a circle increase,area also increase or not?

Answer 1

Yes.

Explanation:

As the diameter of the circle increases, both the area and the circumference of the circle get larger.

Take, for example, a circle with a diameter of `6`, that increases to become a diameter of `7`:

`"Diameter"` `color(white)"xxxx"` `"Area"`

`color(white)"xxx"6` `color(white)"xxxxxxxx"9pi`

`color(white)"xxx"7` `color(white)"xxxxxxxx"12.25pi`

Just increasing the diameter by 1 digit makes the area greater. So yes, as the diameter increases, the area increases.

Answer 2

`color(blue)("Yes")`

Explanation:

The formula for the area of a circle is given by:

`A=pir^2`

Where `r` is the radius, and `pi` is the ratio of the circumference of a circle to its diameter.

Let `D="diameter"` and `r="radius"`

Since the radius is half the diameter, the radius is:

`D/2`

If the diameter increases by a factor `bba`

Then the radius increases by a factor:

`a/2`

And the area increases by a factor:

`(a/2)^2=a^2/4`