SOLUTION: constract a function expressing the volume V of a cube as as function of the length of its diagonal d, where d is the line segment joining opposite non- co- planer vertics of the c

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Question 193523This question is from textbook college algebra
: constract a function expressing the volume V of a cube as as function of the length of its diagonal d, where d is the line segment joining opposite non- co- planer vertics of the cube and d is not a side of the cube.
it is word problem I really dont know how to solve it please help me.
This question is from textbook college algebra

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
construct a function expressing the volume V of a cube as as function of the
length of its diagonal d, where d is the line segment joining opposite
non- co- planer vertices of the cube and d is not a side of the cube.
:
drawing this will help:
The hypotenuse they are talking about is formed by the diagonal of the bottom of the cube and the height of the cube
:
Let x = side of the cube
then
= diagonal of the bottom
and
d =
Which is
d =
d =
Solve for x
d^2 = 3x^2
= x^2
which is
x =
:
v = x^3
Substitute for x:
V(d) = ; is the required function
:
I checked this using x=2, you can do the same

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