Question

The area of a circle is 4 square inches. What is the radius?

Give the exact answer in simplest form.

Answer 1

`\mathrm{From\ figure,}\\\mathrm{Area\ of\ circle=4\pi \ in^2}\\\mathrm{where,\ r\ is\ the\ radius\ of\ circle.}\\\mathrm{or,\ }\pi r^2=4\pi\\\mathrm{or,\ }r^2=4\\\mathrm{or,\ }r=\pm2\\r=-2\mathrm{\ cannot\ be\ possible\ since\ radius\ cannot\ be\ negative.}\\\mathrm{\therefore\ r=2}`

Answer 2

Hello!

Answer:

`\Large \boxed{\sf 2in}`

Explanation:

The formula to calculate the area of a circle is:

`\sf A = \pi r^2`

Where:

`\sf A = area~ of ~the~ circle\\\\r = radius ~of ~the ~circle`

We know that the area of our circle is:

`\sf 4\pi`

So we have this equation, where we want to solve r:

`\sf 4\pi = \pi r^2`

Let's solve r in this equation:

`\sf 4\pi = \pi r^2`

◼ Divide both sides by π:

`\sf (4\pi)/(\pi) =( \pi r^2)/(\pi )`

◼ Simplify both sides:

`\sf 4 = r^2`

◼ We know that if
`\sf x^2 = a`, then
`\sf x=\pm√(a)`:

`\sf √(4) = √(r^2)`

◼ Simplify both sides:

`\sf r = \pm2`

The radius can't be negative so the radius is equal to 2.