Question

A circle has an area of 25 sq. what is the diameter? 100 points

Answer 1

5 sq.

Explanation:

To find the diameter of a circle with an area of 25 square units, we can use the formula: diameter = 2 * √(area / π). Plugging in the numbers, the diameter would be approximately 5 units.

Answer 2

Diameter = 5.64 units

Explanation:

The area (
`\sf A`) of a circle is given by the formula
`\sf A = \pi r^2`, where
`\sf r` is the radius. The diameter (
`\sf D`) is twice the radius (
`\sf D = 2r`).

Given that:

The area of the circle is 25 square units, we can find the radius and then calculate the diameter.

`\sf A = \pi r^2`

Given
`\sf A = 25`.

we can solve for
`\sf r`:

`\sf 25 = \pi r^2`

`\sf r^2 = (25)/(\pi)`

`\sf r = \sqrt{(25)/(\pi)}`

Now, to find the diameter (
`\sf D`):

`\sf D = 2r`

`\sf D = 2 \sqrt{(25)/(\pi)}`

This is the exact expression for the diameter.

If you want a numerical approximation, we can substitute the value of
`\sf \pi` (approximately 3.1415926535897):

`\sf D \approx 2 * \sqrt{(25)/(3.1415926535897)}`

`\sf D \approx 2 * (5)/(3.1415926535897)`

`\sf D \approx 2 * 2.8209479177387`

`\sf D \approx 5.6418958354775`

`\sf D \approx 5.64` ( in 2 d.p.)

So, the diameter of the circle is approximately 5.64 units.