Posted by **Christy** on Sunday, January 12, 2014 at 6:21pm.

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.

- pre-calculus -
**Steve**, Sunday, January 12, 2014 at 6:31pm
d^2 = 3s^2

so, s = (d/3)^(1/2)

v = s^3 = (d/3)^(3/2)

A = 6s^2 = 2d

- pre-calculus -
**Damon**, Sunday, January 12, 2014 at 6:36pm
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

- pre-calculus - typo -
**Steve**, Sunday, January 12, 2014 at 6:38pm
Scratch all that, since

s = d/√3

v = s^3 = d^3/√27

a = 6s^2 = 2d^2

- pre-calculus -
**Damon**, Sunday, January 12, 2014 at 6:40pm
whew :)

- pre-calculus -
**Christy**, Sunday, January 12, 2014 at 6:45pm
thank you :)

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