Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. V= (d) Use the given information to write an equation that relates the variables x and y. (e) Use part (d) to write the volume as a function of only x. V(x) = (f) Finish solving the problem by finding the largest volume that such a box can have. ft3

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. V= (d) Use the given information to write an equation that relates the variables x and y. (e) Use part (d) to write the volume as a function of only x. V(x) = (f) Finish solving the problem by finding the largest volume that such a box can have. ft3

Name: Parts D,E,F Consider the following problem: A box with an open top is
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Description: Parts D,E,F Consider the following problem: A box with an open top is to be constructedfrom a square piece of cardboard, 3 ft wide, by cutting out a square fromeach of the four corners and bending up the sides. Find the largest volumethat such a 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 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

Parts D,E,F

Consider the following problem: A box with an open top is to be constructed
from a square piece of cardboard, 3 ft wide, by cutting out a square from
each of the four corners and bending up the sides. Find the largest volume
that such a box can have.
(a) Draw several diagrams to illustrate the situation, some short boxes
with large bases and some tall boxes with small bases. Find the volumes
of several such boxes.
(b) Draw a diagram illustrating the general situation. Let x denote the
length of the side of the square being cut out. Let y denote the length of
the base.
(c) Write an expression for the volume V in terms of both x and y.
V=
(d) Use the given information to write an equation that relates the
variables x and y.
(e) Use part (d) to write the volume as a function of only x.
V(x) =
(f) Finish solving the problem by finding the largest volume that such a
box can have.
ft3

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