SOLUTION: Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume?

Question 218034: Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Dalton has a closed rectangular box with a square base at least 10 inches long
have a surface area of 900 square inches.
what dimensions will give the box a maximum volume?
;
Let x = the side of the square base
Actually the maximum is when the box is a perfect cube, therefore
let x = the height of the box also
:
Surface area equation, find h:
6x^2 = 900
simplify divide by 6
x^2 = 150
x =
x = 12.247"
:
Max vol: 12.247 by 12.247 by 12.247, and 12.247^3 = 1836.9 cu/in
:
You can prove this:
let the height = h,
:
Surface area equation, find h:
2x^2 + 4xh = 900
simplify divide by 2
x^2 + 2xh = 450
2xh = -x^2 + 450
h =
:
Volume equation
V = x^2 * h
Replace h
V = x^2()
V = x()
V = x()

Graph this equation y=V

:
Shows max volume when x is a little over 12"; vol is about 1800 cu/in

RELATED QUESTIONS
a closed box with a square base is to have a volume of 1,500 cubic inches. Express its... (answered by mananth)

The surface area of a rectangular box with a square base is 54 square inches, and is... (answered by ankor@dixie-net.com)

A closed box with a square base of side x inches is to hold 125 cubic inches. Write the... (answered by ikleyn,josgarithmetic)

A closed box with a square base of side x inches is to hold 125 cubic inches. Write the... (answered by josgarithmetic)

A closed tube is 10 inches long with a radius of 5 inches find its surface area find... (answered by ankor@dixie-net.com)

Volume of a rectangular box with base being 50 square inches and height of 12... (answered by josgarithmetic)

Find possible dimensions for a closed box with volume of 196 cubic centimeters, surface... (answered by bucky)

A box manufacturer is to produce a closed box of volume 4500 cubic inches, where the base (answered by josgarithmetic,ikleyn)

1. Find the width of a rectangular prism that is 12 inches high, 27 inches long, and has... (answered by ewatrrr)