SOLUTION: Information: A rectangular box which is open at the top, has a square base with sides of x cm and a height of h cm. Question: An open rectangular box
Algebra.Com
Question 889186: Information: A rectangular box which is open at the top, has a square base with sides of x cm and a height of h cm. Question: An open rectangular box is to be constructed so that it can hold 256cm cube when completely full. What must its dimensions be so that as little material as possible is used in its construction?
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Volume, .
Total one-sided area, , represents the amount of material making the box. A is the amount of material.
Solve the volume equation for h.
and substitute into A equation.
.
The derivative way to continue for the minimum is . Not sure if you are studying Calculus so here is a try with just arithmetic.
-----------No. I am uncomfortable with this method.
DIFFENTIATING A:
-
, we only need to focus on the numerator to be zero.
----------assuming that this extreme will be for the minimum area.
-
-----------the height dimension for this expected minimum material area.
RELATED QUESTIONS
A box with a rectangular base and no top is formed by cutting squares out of the
corners (answered by josgarithmetic)
An open box with base 14 cm by 18 cm and height 9 cm (external dimensions) is constructed (answered by Glaviolette)
An open box with base 14 cm by 18 cm and height 9 cm (external dimensions) is constructed (answered by greenestamps)
Please help me to solve this word problem:
An open-top rectangular box has a square... (answered by richwmiller)
A box is to be constructed with a rectangular base and a height of 5 cm. If the... (answered by Fombitz)
A square based boxed with an open top into be made from a square piece of cardboard that... (answered by mananth)
A box with an open top is made from a rectangular piece of cardboard by cutting a square... (answered by stanbon)
CALCULUS(MAXIMA AND MINIMA):A RECTANGULAR BOX HAVING A SQUARE BASE AND OPEN AT THE TOP IS (answered by Alan3354,solver91311)
would you please solve the following problem?
Plastic Box A has a square base of area... (answered by math_helper)