SOLUTION: Express the edge length of a cube as a function of the cubes diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Express the edge length of a cube as a function of the cubes diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.      Log On


   

Question 985448: Express the edge length of a cube as a function of the cubes diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
let a=edge
diagonal of face=sqrt%28a%5E2%2Ba%5E2%29=sqrt%282%29a
diagonal of cube=d=sqrt%28%28sqrt%282%29a%29%5E2%2Ba%5E2%29=sqrt%283%29a
.
a=d%2Fsqrt%283%29
Volume=%28d%2Fsqrt%283%29%29%5E3=d%5E3%2F3sqrt%283%29=sqrt%283%29d%5E3%2F9