calculus help

A drinking cup is made in the shape of a right circular cylinder. for a fixed volume, we wish to make the total material used, the circular bottom and the cylindrical side, as small as possible. Find the ratio of the height to the diameter that minimizes the amount of material used. Hint: Express the height and diameter as a function of the radius r and find the value of r that minimizes the amount of material used.

a) find the equation to maximized or minimized.

b) find the solution

c) showing that your solution is an absolute max or min.

I found the answer to be height/diameter=1/2 when I searched online but there was no work shown. I need someone to show me works. thanks!

  1. 👍 0
  2. 👎 0
  3. 👁 231
asked by Layla
  1. see

    http://www.jiskha.com/display.cgi?id=1395265529

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. vol = pi r^2 h
    so
    h = V/(pi r^2)

    area = pi r^2 + 2 pi r h
    area = A = pi r^2 + 2 pi r V/(pi r^2)
    A = pi r^2 + 2 V /r

    dA/dr = 0 = 2 pi r -2 V /r^2

    V / r^2 = pi r
    V = pi r^3
    but
    V = h (pi r^2)
    so
    h (pi r^2) = pi r^3
    h = r
    or
    h = D/2

    1. 👍 0
    2. 👎 0
    posted by Damon
  3. LOL - I do not even remember doing that !

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus help

    A drinking cup is made in the shape of a right circular cylinder. for a fixed volume, we wish to make the total material used, the circular bottom and the cylindrical side, as small as possible. Find the ratio of the height to the

    asked by Temel on April 24, 2014
  2. CALCULUS

    A cone shaped paper drinking cup is to be made from a circular piece of paper of radius 3 inches by cutting out a sector of the circle and gluing the straight edges together. Find the angle of the cut that gives the cup with the

    asked by Sissy on October 20, 2012
  3. Calculus

    A pencil cup with a capacity of 25π in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the material for the side costs 5/8 of the cost of the material for the base, what dimensions should the

    asked by Emily on March 16, 2020
  4. calculus

    A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

    asked by Linda on April 8, 2015
  5. calc (plz, with steps and explanations)

    A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

    asked by Linda on April 9, 2015
  1. calc (with through steps)

    A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

    asked by Linda on April 9, 2015
  2. math (explanation and answer)

    A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

    asked by Linda on April 9, 2015
  3. calculus

    A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way.

    asked by Linda on April 8, 2015
  4. math algebra

    Can someone help me with this question? A can in the shape of a right circular cylinder is required to have a volume of 1,000 cubic centimeters. The top and bottom are made up of a material that costs 10¢ per square centimeter,

    asked by Jacob on February 22, 2016
  5. math

    The interior of a typical mesung cup is a right circular cylinder of radius 6 cm. The volume of water we put in the cup is therefore a function of the level h to which the cup is filled. How closely do we have to measure h to

    asked by ibranian on August 8, 2012

More Similar Questions