A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 2 years ago
all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.
anonymous
 2 years ago
all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.

This Question is Closed

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0looks like a related rate problem fortunately the formula for the volume of a cube is easy, it is \(V(x)=x^3\)

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0take the derivative with respect to time and get \[V'=3x^2x'\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0you are told \(x'=3\) so this is really \[V'=9x^2\] replace \(x\) by the various values to get \(V'\)

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0i used \(V'\) and \(x'\) instead of \(\frac{dV}{dt}\) and \(\frac{dx}{dt}\) because it was easier for me to write also for you it is easier

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0but in your notation, you have \[V=x^3\] so \[\frac{dV}{dt}=3x^2\frac{dx}{dt}\]

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0this line all edges of a cube are expanding at a rate of 3 centimeters per second tells you that \(\frac{dx}{dt}=3\)

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0that means \(\frac{dV}{dt}=3x^2\times 3=9x^2\)

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0let me know if i lost you there
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.