A box is to be made out of a 6 cm by 16 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Draw a labeled sketch. (b) Express the volume V of the box as a function of . V(x) = (c) Give the domain of V in interval notation. Domain= (d) Find the length L, width W, and height of the resulting box that maximizes the volume. (Assume that W≤ L. That is, assume that the widt W of the box is the side formed from the shorter side of cardboard, and the length L of the box is the side formed from the longer side.) L = cm³ cm
A box is to be made out of a 6 cm by 16 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Draw a labeled sketch. (b) Express the volume V of the box as a function of . V(x) = (c) Give the domain of V in interval notation. Domain= (d) Find the length L, width W, and height of the resulting box that maximizes the volume. (Assume that W≤ L. That is, assume that the widt W of the box is the side formed from the shorter side of cardboard, and the length L of the box is the side formed from the longer side.) L = cm³ cm
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A box is to be made out of a 6 cm by 16 cm piece of cardboard. Squares of side length x cm will be cut out of each corner, and then the
ends and sides will be folded up to form a box with an open top.
(a) Draw a labeled sketch.
(b) Express the volume V of the box as a function of x.
V(x) =
(c) Give the domain of V in interval notation.
Domain=
L
(d) Find the length L, width W, and height x of the resulting box that maximizes the volume. (Assume that W ≤ L. That is, assume that the width
W of the box is the side formed from the shorter side of cardboard, and the length L of the box is the side formed from the longer side.)
-
=
W
=
X =
cm
Maximum volume =
(e) Find the maximum volume of the box.
cm
cm
cm³
cm³.
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