calculus

posted by .

A rectangular aquarium is to be built with an open top (no material needed) and a square base. You have 60 square feet of material to build it with. (We are assuming that the sides and bottom are perfectly flat). What is the maximum volume that this aquarium might have? Note-draw a picture, and note that the area of the four sides and bottom can be calculated: this is the amount of material that you will use.

--any help would be very appreciated--

  • calculus -

    let the base by x by x and the height y
    (make a sketch)

    surface area = x^2 + 4xy
    x^2 + 4xy = 60
    y = (60- x^2)/(4x)

    volume= x^2(y) = x^2(60-x^2)/(4x)
    = 15x - (1/4)x^3
    d(volume)/dx = 15 - (3/4)x^2
    = 0 for a max of volume

    (3/4)x^2 = 15
    x^2 = 20
    x = √20

    so max volume = 15√20 - (1/4)20√20 = 10√20 or 20√5

  • calculus -

    thank you very much

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    A rectangular box is to be constructed from two different materials. The box will have a square base and open top. The material for the bottom costs $4.25/m2. The material for the sides costs $2.50/m2. Find the dimensions of the box …
  2. calculus

    a closed box with square base is to have a V= 2000in^3. The material for the top and bottom of the box is to cost $3 per square inch and the material for the sides is the cost $1.50 per square inch. If the cost of the material is to …
  3. Calculus

    AM having problems understanding what equations to use for this word problem. Please help. A rectangular storage container with an open top is to have a volume of 48ft^3. The length of its base is twice the width. Material for the …
  4. Calculus

    A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 37¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 13¢/square foot, determine …
  5. Algebra

    4. A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.00 per square foot and the material for the top costs $1.50 per square …
  6. Calculus

    An open top box with a square base is to be made so that it holds 3 cubic feet. Assuming the material on the base costs $3 per square foot and the material on the sides costs $2 per square foot, determine the size of the base that …
  7. Math

    The public library has an aquarium in the shape of arectangle prism . The base is 6 feet by 2.5 feet and the height is 4 feet . How many square feet of glass were used to build the aquarium (the top of the aquarium is open).
  8. Calculus

    A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square …
  9. Math

    A rectangular box is to have a square base and volume of 78 feet cubed. If the material for the base costs $.30 per square feet, the material for the sides costs $.10 per square foot, and the material for the top costs $.20 per square …
  10. Calculus

    A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs $12 per square meter. Material for the sides costs $5 per square meter. Find the cost …

More Similar Questions