AP Calculus

posted by .

A cardboard box of 108in cubed volume with a square base and no top constructed. Find the minimum area of the cardboard needed. (Optimization)

  • AP Calculus -

    area= s^2+hs

    Volume=s^2*h or 108/s^2=h

    area= s^2+108/s
    dA/ds= 2s-108/s^2=0

    2s^3=108

    solve.

  • AP Calculus -

    Would the answer be 3.7?

  • AP Calculus -

    you are looking for area, finding s is only the first step. Look at the area formula.

  • AP Calculus -

    answer in the back of the book is 180in squared

    but im not getting that answer

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in squares from each corner and folding up the sides... the box is told 100 in cube, how big a piece of cardboard is needed?
  2. Calculus

    A cardboard box of 32in^3 volume with a square base and open top is to be constructed. What is the length of base that will minimize the surface area?
  3. math

    A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 196 in3. How big a piece of cardboard …
  4. Algebra

    A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding …
  5. Maths Calculus

    We want to build a rectangular cardboard box with no top and of given volume V using the least quantity of cardboard. Find the length of the box's edges by fnding the minimum of the total surface function. Verify that the point you …
  6. math

    A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 324 in3. How big a piece of cardboard …
  7. math

    a tray with a square base is to be made from a square piece of cardboard by cutting 5 inch squares from each corner and folding up the sides. If the box is to hold a volume 520 cubic inches, find the length of the piece of cardboard …
  8. Math

    An open-topped box is constructed from a piece of cardboard with a length 2 cm longer than its width. A 6 cm square is cut from each corner and the flaps turned up from the sides of the box. If the volume of the box is 4050 cm3 , find …
  9. Math

    a tray with a square base is to be made from a square piece of cardboard by cutting 5 inch squares from each corner and folding up the sides. If the box is to hold a volume 520 cubic inches, find the length of the piece of cardboard …
  10. Calculus

    A rectangular tank with a square​ base, an open​ top, and a volume of 4,000 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. I'm not understanding how to get started …

More Similar Questions