What is the depth of a cube if its surface area measures 315.375 square inches?

To determine the depth of a cube from its surface area, it's essential to first understand the relationship between the surface area and the dimensions of a cube. The formula to calculate the surface area of a cube is:

[ \text{Surface Area} = 6a^2 ]

where ( a ) is the length of one side of the cube.

Given that the surface area is 315.375 square inches, you can set up the equation:

[ 6a^2 = 315.375 ]

To solve for ( a^2 ), divide both sides by 6:

[ a^2 = \frac{315.375}{6} = 52.5625 ]

Next, take the square root of both sides to find ( a ):

[ a = \sqrt{52.5625} \approx 7.25 ]

Thus, the depth of the cube, which is equivalent to the length of any side of the cube, is approximately 7.25 inches. This calculation supports the answer you've identified, as it is derived directly from the known formula for the surface area of a cube, demonstrating the mathematical reasoning that leads to the depth of 7.25 inches.