A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area & volume of the cube as a function of the diagonal length.
 2 years ago
Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area & volume of the cube as a function of the diagonal length.

This Question is Closed

thatjacksonguy
 2 years ago
Best ResponseYou've already chosen the best response.0Each side of the cube has length x On one face of the cube, the diagonal is found using Pythagorean's Theorem a^2 + b^2 = c^2 Since this is a cube, a= b = x. And c^2 = sqrt(x^2 + x^2) , so c= sqrt(2x^2) Now d, the diagonal of the cube, can be found side it is formed by a triangle with a side of length x and a side of length sqrt(2x^2) So d^2=( sqrt(2x^2))^2 + x^2 d = sqrt(3x^2) Solving for x gives x=sqrt((d^2)/3) Each face has an area of x^2 = (d^2)/3 Surface area = 6 x ((d^2)/3). ( there are 6 faces on a cube) And volume is x^3 = (sqrt((d^2)/3))^3 That was not easy to type up on an iPad!
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.