### Home > PC > Chapter 8 > Lesson 8.1.3 > Problem 8-45

8-45.

Let

*S*be the surface area of a cube with edge length*L*. Homework Help ✎Write

*S*as a function of*L*.If

*D*is the length of the longest diagonal of the cube, write*D*as a function of*L*.Write

*D*as a function of*S*.

*S* = 6*L*^{2}

Draw a triangle within the cube with the longest diagonal *D*.

Find the diagonal of the bottom square *AC*.

Solve for *L* in your equation from part (a) above. Then substitute that expression for *L* in your *D* equation.

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