SOLUTION: The total surface area of a cube is 10,648 centimeters squared. What is the length of a diagonal that is not a diagonal of a face? Note: The surface area of a cube is 6e squared

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Question 290732: The total surface area of a cube is 10,648 centimeters squared. What is the length of a diagonal that is not a diagonal of a face?
Note: The surface area of a cube is 6e squared, where e is the edges of the cube.
Please help, thank you!
Found 2 solutions by richwmiller, ankor@dixie-net.com:
Answer by richwmiller(17219) (Show Source):
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Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The total surface area of a cube is 10,648 centimeters squared. What is the length of a diagonal that is not a diagonal of a face?
Note: The surface area of a cube is 6e squared, where e is the edges of the cube.
:
Find the diagonal of the face (c)
c^2 = 2e^2
;
Diagonal (d) of opposite corners (not a diagonal of a face)
Using the diagonal of the face and one edge
d^2 = 2e^2 + e^2
d^2 = 3e^2
d =
Find e^2
e^2 =
e^2 = 1774.67
then
d =
d = 72.9658