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

8-45.

Let be the surface area of a cube with edge length

*.*

Write

as a function of.A cube has six square sides of length

. What is the area of each square?If

is the length of the longest diagonal of the cube, write an equation foras a function of.Draw a triangle within the cube with the longest diagonal

.Write an equation for the diagonal of the bottom square

.Write an equation for the longest diagonal,

. Write

as a function of. Solve for

in your equation from part (a) above. Then substitute that expression forinto yourequation.

Use the eTool below to solve this problem.

Click the link at right for the full version of the eTool: *8-45 HW eTool*