Hello, reiward!
Did you make a sketch?
A square is inscribed in a small circle of a sphere with radius 9 cm.
If the plane of the square is 6cm from the center of the sphere,
find the perimeter of the square. Code:
* * *
* | x *
A o - - - + - - - o B
* | * *
6| *
* | * 9 *
* o *
* C *
* *
* *
* *
* * *
$\displaystyle AB$ is the side of the square.
Pythagorus says: .$\displaystyle x^2 + 6^2 \:=\:9^2 \quad\Rightarrow\quad x^2 \:=\:45 \quad\Rightarrow\quad x \:=\:3\sqrt{5}$
. . Then: .$\displaystyle AB \;=\;2x \;=\;6\sqrt{5}$
The perimeter is: .$\displaystyle 4\left(6\sqrt{5}\right) \;=\;24\sqrt{5}\text{ cm}$