Results 1 to 4 of 4

Math Help - Can someone help me with a calculus word problem?

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Can someone help me with a calculus word problem?

    I really don't know how to do the following problem:

    A conical bin must have a volume of 2500 ft3. The circular base is made of a concrete slab, which will cost $1.30 per square foot, and the material for the side costs $3.50 per square foot. Find the dimensions that minimize the total cost.

    I am in an introductory math course and he said to solve this using calculus... how do I start? Am I supposed to take the floor cost multiplied by the side cost? If anyone could give me some helpful hints or the correct answer, I'd really appreciate it. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2009
    Posts
    166
    V = \pi r^2h = 2500

    You want a function for cost.

    V' = SA = 2\pi rh + \pi r^2

    Where the cost of the side is 3.5 and the ends .65 (to account for only one base at 1.30)

    C = 2(3.5)\pi rh + 0.65\pi r^2

    h = \frac{V}{\pi r^2}

    C = 2(3.5)\pi r\frac{V}{\pi r^2} + 0.65\pi r^2 = \frac{7V}{r} + 0.65\pi r^2

    C' = \frac{-7V}{r^2} + 1.30\pi r

    C' = \frac{1.30\pi r^3 - 7V}{r^2}

    \frac{1.30\pi r^3 - 7V}{r^2} = 0

    1.30\pi r^3 - 7V = 0

    Plug in for V, finish calculating r, get your dimensions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,044
    Thanks
    885
    hate to spoil such a great response, but ...

    A conical bin must have a volume ...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2009
    Posts
    166
    Wow. =p Well, I'm pretty sure my 0.65 should've stayed a 1.3 for the cost function.

    I'll make another response soon if someone else doesn't decide to.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculus word problem help.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2010, 05:20 AM
  2. Word Problem-Calculus
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 1st 2010, 01:15 PM
  3. Please help me I have a calculus word problem?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2010, 05:02 PM
  4. Calculus Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 25th 2009, 03:12 PM
  5. Need Calculus Word Problem Help Really Bad!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 11th 2008, 09:01 PM

Search Tags


/mathhelpforum @mathhelpforum