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

Give the exact answer in simplest form.

The area of a circle is 4 square inches. What is the radius? Give the exact answer-example-1
User Sraw
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2 Answers

1 vote

Answer:


\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}

User Brad Johnson
by
7.4k points
4 votes

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.

User Igor Damiani
by
8.3k points

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