A box with an open top has vertical sides, a square bottom and a volume of 4 cubic meters. If the box has the least possible surface area find its dimensions. First the surface area of the open box as a function of x and h where x represents the length of the sides of the squares base and h the height of the open box.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 49E: A diagonal of a cube joins two vertices so that the remaining points of the diagonal lie in the...
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Can you box the answers please
- Part 1: Find the surface area of the open box as a function of x and h, where x represents the length of the sides of the square base
and h the height of the open box.
A(x, h) = x^2+4xh
- Part 2: Find the volume of the open box as a function of x and h.
V(x, h) =
Part 3: Find the value of h as a function of x, using the given value of the volume.
Part 4: Rewrite the surface area of the open box as a function of x only.
Part 5: Find the derivative of the surface area of the open box with respect to x.
Part 6: Find the height and length values that minimize the surface area of the open box.
Transcribed Image Text:- Part 1: Find the surface area of the open box as a function of x and h, where x represents the length of the sides of the square base and h the height of the open box. A(x, h) = x^2+4xh - Part 2: Find the volume of the open box as a function of x and h. V(x, h) = Part 3: Find the value of h as a function of x, using the given value of the volume. Part 4: Rewrite the surface area of the open box as a function of x only. Part 5: Find the derivative of the surface area of the open box with respect to x. Part 6: Find the height and length values that minimize the surface area of the open box.
A box with an open top has vertical sides, a
square bottom and a volume of 4 cubic
meters. If the box has the least possible
surface area find its dimensions.
First the surface area of the open box as a
function of x and h where x represents the
length of the sides of the squares base and h
the height of the open box.
Transcribed Image Text:A box with an open top has vertical sides, a square bottom and a volume of 4 cubic meters. If the box has the least possible surface area find its dimensions. First the surface area of the open box as a function of x and h where x represents the length of the sides of the squares base and h the height of the open box.
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