<p>How do you solve questions like that?</p>
<p>What’s the question?</p>
<p>They gave the radius of the sphere within a cube and then asked us what the longest distance within the cube was I think.</p>
<p>The longest distance is the diagonal. The diameter of the sphere is the side length of the cube. The length of the cube’s diagonal is the side length times the square root of 3, according to the 3-d Pythagorean theorem</p>
<p>Here’s a simple explanation:</p>
<p>[A</a> diagonal in a cube](<a href=“404 Not Found”>A diagonal in a cube)</p>
<p>As far as a formula, one needs the one for the diagonal of a rectangular prism. For instance, for a “box” with dimensions x by y by z, one would use this: </p>
<p>d^2 = x^2 + y^2 + z^2 </p>
<p>For a cube, the dimensions are expressed as x by x by x --making the formula simpler </p>
<p>d^2 = x^2 + x^2 + x^2
d^2 = 3x^2
d = root(3)*x</p>
<p>The question was what is the radius of a sphere inscribed in a cube with side length 2. The answer of course is 1 because the side length is equal to the diameter of the sphere making the radius half that.</p>