Question

A circular disc has an area that measures between 1,650 and 1,700 square inches. What could be the length of its radius?

Answer 1

Let r = radius of the circular disk
`22.92 < r < 23.26` inches

Explanation:

The formula for the area of a circle is `A = pi r^2`, where
r= the radius of the circle
A= the area of the circle
At the moment the variable `r` is unknown for the circular disk, but we do know `A`, which means we can solve the equation like this:
`1650= pi r^2`, divide both sides by `pi` to get
`525.211~~ r^2`, take the square root (`sqrt`) of both sides to get
`22.917489~~ r`. We have the minimum value for the variable `r`.

Now we need to get the maximum value, which we do by using the same process, so
`1700= pi r^2`, divide both sides by `pi` to get
`541.127~~ r^2`, take the square root (`sqrt`) of both sides to get
`23.26213~~ r`

The last thing to do is round up the numbers to the nearest hundredth, because extra precision is not necessary for questions like this. This leaves us with the radius of the circle being higher then 22.92, but lower then 23.26. Translate this into mathematical terms, and you get `22.92 < r < 23.26`

I hope that helped!