A spherical box has surface area $528\text{cm}{2}^{}$. Find the radius of the spherical box.

To find the radius of the spherical box, we start by using the formula for the surface area of a sphere:

$A=4\pi r^2$

where $A$ is the surface area and $r$ is the radius.

Given that the surface area is $528{\text{cm}}^2$, we can substitute this value into the equation. We also use the standard approximation for pi:
$\pi \approx \frac{22}{7}$

Substituting these values, we get:
$528=4\times \frac{22}{7}\times r^2$

Simplify the multiplication on the right-hand side:
$528=\frac{88}{7}\times r^2$

To solve for $r^2$, multiply both sides by 7 and divide by 88:
$r^2=\frac{528\times 7}{88}$

First, calculate the division:
$\frac{528}{88}=6$

Now multiply by 7:
$r^2=6\times 7$
$r^2=42$

Taking the square root of both sides to find the radius $r$:
$r=\sqrt{42}\text{cm}$

Therefore, the correct option is √42 cm.