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<p>The bottom face of the cube would be 8<em>2^(1/2) since that’s a 45-45-90 triangle.
The height of the cube is 8.
Visualize to yourself a triangle that extends from the corner of a cube to the opposite corner. This is essentially the hypotenuse for the triangle that you just made with the bottom face and the height. You can find the length of this hypotenuse through Pythagorean theorem. It comes out to 8</em>3^(1/2), which is twice the distance from the center, so you can divide it be 2 and you’ll get 4*3^(1/2), so A</p>
<p>Alternatively, since you know the length of an edge of the cube is 8, you know that the radius of the sphere is 4. To get to an edge of the cube from the center, you can move four units to the right, four units up, and then another four units towards the corner of the cube. Applying the distance formula, this is root(4^2 + 4^2 + 4^2) which comes out to 4root3.</p>