My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 10th, 2012, 03:45 AM   #1
Senior Member
 
Joined: Jan 2010

Posts: 205
Thanks: 0

Rate problem

Quote:
A snowball melts in volume @ 1 cm³/min. At what rate is the diameter decreasing when the diameter is 10 cm?
Volume of a sphere:
Volume of a sphere in terms of diameter:

Rate of volume:

Rate of diameter:

I'm not sure what to do at this point
daigo is offline  
 
July 10th, 2012, 05:14 AM   #2
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Rate problem

[color=#000000]



when d=10cm at the time instant then

[/color]
ZardoZ is offline  
July 10th, 2012, 05:28 AM   #3
Senior Member
 
Joined: Jan 2010

Posts: 205
Thanks: 0

Re: Rate problem

ZardoZ, how were you able to just put in (time) into the equation of the volume? I don't see how you can get the function Volume(time)
daigo is offline  
July 10th, 2012, 11:02 AM   #4
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Rate problem

Hello, daigo!

Quote:

I would put everything in terms of the radius, and switch to the diameter at the end.











soroban is offline  
July 10th, 2012, 11:11 AM   #5
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Rate problem

You correctly found the volume V as a function of the diameter d is:



Differentiate with respect to time t:



We are given:

hence:



Thus, we find:



And so:

MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
problem, rate



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Derivative/rate problem daigo Calculus 4 July 14th, 2012 09:36 AM
Rate problem daigo Algebra 9 March 1st, 2012 12:07 AM
Please help with this rate differentiation problem! I've tri rockit_hiro Calculus 7 October 27th, 2011 04:29 PM
a man can run...(rate problem) warqzaka Algebra 6 July 21st, 2011 04:23 PM
work rate problem e81 Algebra 2 May 15th, 2011 10:54 AM





Copyright © 2019 My Math Forum. All rights reserved.