# Square units of area in a circle

I'm studying for the GRE and came across the practice question quoted below. I'm having a hard time understanding the meaning of the words they're using. Could someone help me parse their language?

"The number of square units in the area of a circle '$X$' is equal to $16$ times the number of units in its circumference. What are the diameters of circles that could fit completely inside circle $X$?"

For reference, the answer is $64$, and the "explanation" is based on $\pi r^2 = 16(2\pi r).$

Thanks!

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Let the diameter be $d$. Then the number of square units in the area of the circle is $(\pi/4)d^2$. This is $16\pi d$. That forces $d=64$.
The area of a circle of radius $r$ is, as you mentioned, $\pi r^2$. So the area of a circle of diameter $d$ is $\pi(d/2)^2$, We coudld have instead worked with $r$, and translated to diameter at the end. Yes, "the number of square units in the area of" is a fancy way of saying "the area of." –  André Nicolas Jul 2 '12 at 3:53