precalculus
posted by Christy .
Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.

d^2 = 3s^2
so, s = (d/3)^(1/2)
v = s^3 = (d/3)^(3/2)
A = 6s^2 = 2d 
edge length s
diagonal of a side = s sqrt 2
then right triangle with legs s and s sqrt 2
d^2 = s^2 + 2 s^2 = 3 s^2
d = s sqrt 3
s = d/ sqrt 3 = d (3)^.5
area = 6s^2 = 6d^2 (3)1 = 6d^2/3 =2 d^2
vol=s^3=[d(3^.5)]^3 = d^3 /(3 sqrt 3)
= (d^3 sqrt 3)/9 
Scratch all that, since
s = d/√3
v = s^3 = d^3/√27
a = 6s^2 = 2d^2 
whew :)

thank you :)
Respond to this Question
Similar Questions

math
A cube with edges of length 2 centimeters is buildt from centimeter cubes. If you paint the faces of this cube and then break it into centimeter cubes, how many cubes wil be painted on three faces? 
algebra
First: solve for k. Then, go back to the original equation c=k(d3) and solve for c when d is ten. Second: Area=k*s^2 Put in the fist conditions, solve for k. Then, knowing k, solve for A when is eight. direct variation 1)if c varies … 
Math
consider a triangle with vertices (a,b), (c,d), (e,f), with the area of the triangle b/2 a = area of an equilateral triangle with side length b c = length of diagonal of a cube with side length b a/c = the positive asymptote of the … 
algebra
the cube root of the volume of a cube gives the length of one side of the cube. volume=343cm cubed a. find the side length of the cube shown b. find the area of each face of the cube i have no idea how to do this! 
Geometry
A cube has edge lengths of 6 inches. What is the approximate length of a diagonal "d" of the cube? 
Math
damn i cant post a drawing..there r 2 cubes, cube x and cube y and the length of the cube x is 12cm. A) find the volume of cube x. B) if cube y has a volume equal to 1/8 of the volume of cube x, find the length of its edge. 
math
Which of the following is a formula for finding the volume of a cube? 
PreCalc (Point of Inter.)
A diagonal of a cube is a line segment of maximum length whose endpoints are vertices of the cube. To the nearest degree, what is the angle of intersection Ѳ, 0 < Ѳ <= 90° between two distinct diagonals of the same … 
Math
A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere. The edge length of the cube is 5.8 cm. What is the volume of air in the cube to the nearest cubic centimetre? 
geometry
A cube has edge lengths of 4 inches. What is the approximate length of a diagonal "d" of the cube?