Calculus

posted by .

A cylindrical metal can is made to hold 500ml of soup. Determine the dimensions of the can that will minimize the amount of metal required(assume that the top and sides of the can are made from metal of the same thickness

  • Calculus -

    half a liter
    liter is 10*10*10 = 1,000 cm^3

    a = 2(pi r^2) + 2 pi r h
    v = pi r^2 h =500
    so
    h = 500/(pi r^2)
    a = 2 pi r^2 + 1000/r

    da/dr = 0 = 4 pi r - 1000/r^2
    pi r = 500/r^2
    pi r^3 = 500
    r^3 = 500/pi
    r = 5.4 cm
    h = 5.4 cm

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $2/ft2. The metal for the four rectangular sides costs $3/ft2. Find the dimensions that minimize cost if the box …
  2. calculus

    A cylindrical metal can with an open top is to be constructed. the can must have a capacity of 24pie cubic inches. the metal used to contruct the bottom of the can costs 3 times as much as the metal in the rest of the can. Find the …
  3. calculus

    A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $4 per square foot and the metal for the sides costs $4 per square foot. Find the dimensions that minimize cost …
  4. Calculus

    A box is constructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $2 per square foot and the metal for the sides costs $7 per square foot. Find the dimensions that minimize cost …
  5. Calculus

    A metal cylindrical container with an open top is to hold 1 cubic foot. If there is no waste in construction, find the dimensions which will require the least amount of material.
  6. physics

    A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal every where is 0.4 cm thick. Calculate the volume of the metal correct to 1 place of decimal
  7. physics

    A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal every where is 0.4 cm thick. Calculate the volume of the metal correct to 1 place of decimal
  8. calculus

    A box is contructed out of two different types of metal. The metal for the top and bottom, which are both square, costs $5 per square foot and the metal for the sides costs $2 per square foot. Find the dimensions that minimize cost …
  9. Mathematics

    A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its height is 25 cm. If thickness of the metal is 8mm everywhere, calculatd the volume of metal in the cylinder
  10. Calculus

    Gloria would like to construct a box with volume of exactly 45ft^3 using only metal and wood. The metal costs $15/ft^2 and the wood costs $6/ft^2. If the wood is to go on the sides, the metal is to go on the top and bottom, and if …

More Similar Questions