A box with a square base and an open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of material used.
- print Print
- list Cite
Expert Answers
thilina-g
| Certified Educator
calendarEducator since 2011
write596 answers
starTop subjects are Math and Science
Let the width of the square base be x and height of the box be y, then
Volume, V is given by,
`V = x^2y`
The area (or amount of material), A is given by,
`A = x^2+4(xy)`
Now we have to find values for x and y, such that it A has a minimum with volume of 32000`cm^3`
`32000 = x^2y`
`y = 32000/x^2`
If we substitute this in A,
`A = x^2+4x(32000/x^2)`
`A =...
(The entire section contains 180 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- A rectangular box with a square base and open top is to be made from 1200 cm^2 of material. Find...
- 1 Educator Answer
- If a box with a square base and open top is to have a volume of 4 ft^3,find the dimensions that...
- 1 Educator Answer
- A box with a square base and no top must have a volume of 10 000 cm^3. If the smallest dimension...
- 1 Educator Answer
- Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,...
- 1 Educator Answer
- Open-top boxes are constructed by cutting equal squares from the corners of cardboard sheets that...
- 1 Educator Answer