**Q: The area of a circle is 16π cm squared. What is the diameter of the circle?**

Answer:

First we need to know the area formula for a circle… This is:

A = π*r^{2} [r is the radius]

Since the area is given to us, we can plug that in to the formula to get:

16*π = π*^{2}

The only variable is r, so we can use algebra to solve for r like so:

Divide both sides by π (which makes the π’s cancel out):

16*π **/π** = π*r^{2} **/π**

16 = r^{2}

Now, take the square root of both sides to solve for r:

√(16) = r

4 = r [remember, the square root of 16 is actually +4 or -4, however, since we are taking about a radius which is a length, only +4 makes sense as an answer.]

So, the radius of the circle is 4. The diameter is 2*radius… So, the **diameter is 8 cm.**

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