A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 300 m and the minimum diameter, 500 m above the base, is 200 m. Find an equation for the tower. (Assume the center is at the origin with axis the zaxis and the minimum diameter is at the center.)
anonymous
 one year ago
A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 300 m and the minimum diameter, 500 m above the base, is 200 m. Find an equation for the tower. (Assume the center is at the origin with axis the zaxis and the minimum diameter is at the center.)

This Question is Open

Clalgee
 one year ago
Best ResponseYou've already chosen the best response.4Alright, Since minimum diameter is at z = 500, then centre of hyperboloid is (0, 0, 500). Right? Now here is the equation for hyperboloid: \[x^2/A^2 + y^2/B^2  (z  500)^2 / C^2 = 1\] Horizontal Crosssections are circles in other words: A = B New equation: \[x^2/A^2 + y^2/A^2  (z  500)^2 / C^2 = 1\]

Clalgee
 one year ago
Best ResponseYou've already chosen the best response.4When z = 500, radius = 200/2 = 100 \[x^2 / A^2 + y^2 / B^2  (500  500)^2 / C^2 = 1\] \[x^2 / A^2 + y^2 /A^2 = 1\] A= 100

Clalgee
 one year ago
Best ResponseYou've already chosen the best response.4When z = 0, radius = 300/2 = 150 (crosssection: x² + y² = 150²) \[x^2 / 100^2 + y^2 / 100^2  (0  500)^2 / C^2 = 1\] \[x^2 / 100^2 + y^2 = 500^2 / C^2 + 1\] \[x^2 + y^2 = 100^2 (500^2 / C^2 + 1) = 150^2\] \[100^2 (500^2 / C^2 + 1) = 150^2 \] \[(500^2 / C^2 + 1) = 150^2 /100^2 = 9/4 \] \[500^2 / C^2 = 5/4\] \[C^2 / 500^2 = 4/5 \] ^ Multiply Above \[C^2 = 200,000 \] Lastly: x²/10,000 + y²/10,000 − (z−500)²/200,000 = 1
Ask your own question
Sign UpFind 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.