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

Algebra ->  Algebra  -> Volume -> 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      Log On

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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(7696) About Me  (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
sqrt%282x%5E2%29 = diagonal of the bottom
and
d = sqrt%28%28sqrt%282x%5E2%29%29%5E2+%2B+x%5E2%29
Which is
d = sqrt%282x%5E2+%2B+x%5E2%29
d = sqrt%283x%5E2%29
Solve for x
d^2 = 3x^2
d%5E2%2F3 = x^2
which is
x = sqrt%28d%5E2%2F3%29
:
v = x^3
Substitute sqrt%28d%5E2%2F3%29 for x:
V(d) = %28sqrt%28d%5E2%2F3%29%29%5E3; is the required function
:
I checked this using x=2, you can do the same