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.
:
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 = {{{sqrt(3e^2)}}}
Find e^2
e^2 = {{{10648/6}}}
e^2 = 1774.67
then
d = {{{sqrt(3*1774.67)}}}
d = 72.9658