A cube is inscribed in a sphere of diameter 'd' cm. What is the side of the largest cube so inscribed?

Answer

To find the side length of the largest cube inscribed in a sphere of diameter \( d \) cm, we can follow these steps:

### Step 1: Understand the relationship between the cube and the sphere
When a cube is inscribed in a sphere, the diagonal of the cube is equal to the diameter of the sphere.

### Step 2: Calculate the diagonal of the cube
Let the side length of the cube be \( x \). The formula for the diagonal \( D \) of a cube with side length \( x \) is given by:
\[ D = x \sqrt{3} \]

### Step 3: Set the diagonal equal to the diameter of the sphere
Since the diagonal of the cube is equal to the diameter of the sphere, we can write:
\[ x \sqrt{3} = d \]

### Step 4: Solve for the side length \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{d}{\sqrt{3}} \]

### Conclusion
Thus, the side length of the largest cube that can be inscribed in a sphere of diameter \( d \) cm is:
\[ \boxed{\frac{d}{\sqrt{3}}} \]