Q: The area of a circle is 16π cm squared. What is the diameter of the circle?
First we need to know the area formula for a circle… This is:
A = π*r2 [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*r2 /π
16 = r2
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.