If the sum of the squares of the distances of a point $P(x, y, z)$ from the three co-ordinate axes is 324 , then the distance of point $P$ from the origin is ....

Distance from the origin: A point $P(x, y, z)$ has an origin distance of $\sqrt{x^2 + y^2 + z^2}$.

Sum of squared axis distances: The squared distances from the axes are $y^2 + z^2$, $x^2 + z^2$, and $x^2 + y^2$. Their sum is given as 324.

Combine terms: $2x^2 + 2y^2 + 2z^2 = 324$, so $x^2 + y^2 + z^2 = 162$.

Thus, the distance is $\sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2}$.

The correct option is C.