Explanation Formula used: The surface area of the cardboard used to make the box is Area of four sides +Base area . Volume of the cuboidal box is V = Length×Breath×Height . Calculation: Consider a box with a square base of side x ft and an open square top congruent to the base. Let the height of the cuboidal box be y ft . The surface area of the cardboard used to make the box is 27 ft 2 . Ans also surface area of the cardboard used to make the box is ( 4 x y + x 2 ) . Thus, compare the both statement: ( 4 x y + x 2 ) = 27 y = 27 − x 2 4 x From the second formula, the volume of the cuboidal box is calculated as: V = Length×Breath×Height = x × x × y = x 2 y The value of y substitute in volume equation. V = x 2 y = x 2 × ( 27 − x 2 4 x ) = x × ( 27 − x 2 4 ) = ( 27 x − x 3 4 ) For the maximum value of volume, differentiate the volume function with respect to x and evaluate to 0 as follows: d V d x = 0 d d x

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

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Chapter 24, Problem 83RE

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The maximum volume that can be contained within the box.

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Chapter 24, Problem 82RE

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Chapter 24 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. EXAMPLE...Ch. 24.2 - Prob. 1E Ch. 24.2 - Prob. 2E Ch. 24.2 - Prob. 3E Ch. 24.2 - Prob. 4E Ch. 24.2 - Prob. 5E Ch. 24.2 - Prob. 6E Ch. 24.2 - Prob. 7E Ch. 24.2 - Prob. 8E Ch. 24.2 - Prob. 9E Ch. 24.2 - Prob. 10E Ch. 24.2 - Prob. 11E Ch. 24.2 - Prob. 12E Ch. 24.2 - Prob. 13E Ch. 24.2 - Prob. 14E Ch. 24.2 - Prob. 15E Ch. 24.2 - Prob. 16E Ch. 24.2 - Prob. 17E Ch. 24.2 - Prob. 18E Ch. 24.2 - Prob. 19E Ch. 24.2 - Prob. 20E Ch. 24.2 - Prob. 21E Ch. 24.2 - Prob. 23E Ch. 24.2 - Prob. 24E Ch. 24.2 - Prob. 25E Ch. 24.2 - Prob. 27E Ch. 24.2 - Prob. 28E Ch. 24.2 - Prob. 29E Ch. 24.2 - Prob. 30E Ch. 24.3 - Prob. 1PE Ch. 24.3 - Prob. 1E Ch. 24.3 - Prob. 2E Ch. 24.3 - Prob. 3E Ch. 24.3 - Prob. 4E Ch. 24.3 - Prob. 5E Ch. 24.3 - Prob. 6E Ch. 24.3 - Prob. 7E Ch. 24.3 - Prob. 8E Ch. 24.3 - Prob. 9E Ch. 24.3 - Prob. 10E Ch. 24.3 - Prob. 11E Ch. 24.3 - Prob. 12E Ch. 24.3 - Prob. 13E Ch. 24.3 - Prob. 14E Ch. 24.3 - Prob. 15E Ch. 24.3 - Prob. 16E Ch. 24.3 - In Exercises 11–30, find the indicated velocities...Ch. 24.3 - Prob. 18E Ch. 24.3 - Prob. 19E Ch. 24.3 - Prob. 20E Ch. 24.3 - Prob. 21E Ch. 24.3 - Prob. 22E Ch. 24.3 - Prob. 23E Ch. 24.3 - Prob. 24E Ch. 24.3 - Prob. 25E Ch. 24.3 - Prob. 26E Ch. 24.3 - Prob. 27E Ch. 24.3 - Prob. 28E Ch. 24.3 - Prob. 29E Ch. 24.3 - Prob. 30E Ch. 24.4 - In Example 2, change each 10 to 12, and then...Ch. 24.4 - In Exercises 1 and 2, make the given changes in...Ch. 24.4 - In Exercises 1 and 2, make the given changes in...Ch. 24.4 - In Exercises 3–6, assume that all variables are...Ch. 24.4 - In Exercises 3–6, assume that all variables are...Ch. 24.4 - In Exercises 3–6, assume that all variables are...Ch. 24.4 - In Exercises 3–6, assume that all variables are...Ch. 24.4 - Prob. 7E Ch. 24.4 - Prob. 8E Ch. 24.4 - Prob. 9E Ch. 24.4 - Prob. 10E Ch. 24.4 - Prob. 11E Ch. 24.4 - Prob. 12E Ch. 24.4 - Prob. 13E Ch. 24.4 - Prob. 14E Ch. 24.4 - Prob. 15E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 17E Ch. 24.4 - Prob. 18E Ch. 24.4 - Prob. 19E Ch. 24.4 - Prob. 20E Ch. 24.4 - Prob. 21E Ch. 24.4 - Prob. 22E Ch. 24.4 - Prob. 23E Ch. 24.4 - Prob. 24E Ch. 24.4 - Prob. 25E Ch. 24.4 - Prob. 26E Ch. 24.4 - Prob. 27E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 31E Ch. 24.4 - Prob. 32E Ch. 24.4 - Prob. 33E Ch. 24.4 - Prob. 34E Ch. 24.4 - Prob. 35E Ch. 24.4 - Prob. 36E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 38E Ch. 24.4 - Prob. 39E Ch. 24.4 - Prob. 40E Ch. 24.4 - Prob. 41E Ch. 24.4 - Prob. 42E Ch. 24.5 - Prob. 1PE Ch. 24.5 - Prob. 2PE Ch. 24.5 - Prob. 1E Ch. 24.5 - Prob. 2E Ch. 24.5 - Prob. 3E Ch. 24.5 - Prob. 4E Ch. 24.5 - Prob. 5E Ch. 24.5 - Prob. 6E Ch. 24.5 - Prob. 7E Ch. 24.5 - Prob. 8E Ch. 24.5 - Prob. 9E Ch. 24.5 - Prob. 10E Ch. 24.5 - Prob. 11E Ch. 24.5 - Prob. 12E Ch. 24.5 - Prob. 13E Ch. 24.5 - Prob. 14E Ch. 24.5 - Prob. 15E Ch. 24.5 - Prob. 16E Ch. 24.5 - 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A microprocessor chip is being designed with a...Ch. 24.7 - Prob. 18E Ch. 24.7 - What are the dimensions of the largest rectangular...Ch. 24.7 - A rectangular storage area is to be constructed...Ch. 24.7 - Prob. 21E Ch. 24.7 - Prob. 22E Ch. 24.7 - Prob. 23E Ch. 24.7 - Prob. 24E Ch. 24.7 - Prob. 25E Ch. 24.7 - Prob. 26E Ch. 24.7 - Prob. 27E Ch. 24.7 - Prob. 28E Ch. 24.7 - Prob. 29E Ch. 24.7 - Prob. 30E Ch. 24.7 - Prob. 31E Ch. 24.7 - Prob. 32E Ch. 24.7 - Prob. 33E Ch. 24.7 - What is the minimum slope of the curve y = x5 −...Ch. 24.7 - Prob. 35E Ch. 24.7 - Prob. 36E Ch. 24.7 - Prob. 37E Ch. 24.7 - Prob. 38E Ch. 24.7 - Prob. 39E Ch. 24.7 - Prob. 40E Ch. 24.7 - Prob. 41E Ch. 24.7 - Computer simulation shows that the drag F (in N)...Ch. 24.7 - Prob. 43E Ch. 24.7 - The potential energy E of an electric charge q due...Ch. 24.7 - An open box is to be made from a square piece of...Ch. 24.7 - Prob. 46E Ch. 24.7 - Prob. 47E Ch. 24.7 - Prob. 48E Ch. 24.7 - An oil pipeline is to be built from a refinery to...Ch. 24.7 - Prob. 50E Ch. 24.7 - Prob. 51E Ch. 24.7 - Prob. 52E Ch. 24.7 - Prob. 53E Ch. 24.7 - Prob. 54E Ch. 24.8 - Prob. 1PE Ch. 24.8 - Prob. 2PE Ch. 24.8 - Prob. 1E Ch. 24.8 - Prob. 2E Ch. 24.8 - Prob. 3E Ch. 24.8 - Prob. 4E Ch. 24.8 - Prob. 5E Ch. 24.8 - Prob. 6E Ch. 24.8 - Prob. 7E Ch. 24.8 - Prob. 8E Ch. 24.8 - Prob. 9E Ch. 24.8 - Prob. 10E Ch. 24.8 - Prob. 11E Ch. 24.8 - Prob. 12E Ch. 24.8 - Prob. 13E Ch. 24.8 - Prob. 14E Ch. 24.8 - Prob. 15E Ch. 24.8 - Prob. 16E Ch. 24.8 - Prob. 17E Ch. 24.8 - Prob. 18E Ch. 24.8 - Prob. 19E Ch. 24.8 - Prob. 20E Ch. 24.8 - Prob. 21E Ch. 24.8 - Prob. 22E Ch. 24.8 - Prob. 23E Ch. 24.8 - Prob. 24E Ch. 24.8 - Prob. 25E Ch. 24.8 - Prob. 26E Ch. 24.8 - Prob. 27E Ch. 24.8 - Prob. 28E Ch. 24.8 - Prob. 29E Ch. 24.8 - Prob. 30E Ch. 24.8 - Prob. 31E Ch. 24.8 - Prob. 32E Ch. 24.8 - Prob. 33E Ch. 24.8 - Prob. 34E Ch. 24.8 - Prob. 35E Ch. 24.8 - Prob. 36E Ch. 24.8 - Prob. 37E Ch. 24.8 - Prob. 38E Ch. 24.8 - Prob. 39E Ch. 24.8 - Prob. 40E Ch. 24.8 - Prob. 41E Ch. 24.8 - Prob. 42E Ch. 24.8 - Prob. 43E Ch. 24.8 - Prob. 44E Ch. 24 - Prob. 1RE Ch. 24 - Prob. 2RE Ch. 24 - Prob. 3RE Ch. 24 - Prob. 4RE Ch. 24 - Prob. 5RE Ch. 24 - Prob. 6RE Ch. 24 - Prob. 7RE Ch. 24 - Prob. 8RE Ch. 24 - Prob. 9RE Ch. 24 - Prob. 10RE Ch. 24 - Prob. 11RE Ch. 24 - Prob. 12RE Ch. 24 - Prob. 13RE Ch. 24 - Prob. 14RE Ch. 24 - Prob. 15RE Ch. 24 - Prob. 16RE Ch. 24 - Prob. 17RE Ch. 24 - Prob. 18RE Ch. 24 - Prob. 19RE Ch. 24 - Prob. 20RE Ch. 24 - Prob. 21RE Ch. 24 - Prob. 22RE Ch. 24 - Prob. 23RE Ch. 24 - Prob. 24RE Ch. 24 - Prob. 25RE Ch. 24 - Prob. 26RE Ch. 24 - Prob. 27RE Ch. 24 - In Exercises 25–32, sketch the graphs of the given...Ch. 24 - Prob. 29RE Ch. 24 - Prob. 30RE Ch. 24 - Prob. 31RE Ch. 24 - Prob. 32RE Ch. 24 - Prob. 33RE Ch. 24 - Prob. 34RE Ch. 24 - Prob. 35RE Ch. 24 - Prob. 36RE Ch. 24 - Prob. 37RE Ch. 24 - Prob. 38RE Ch. 24 - Prob. 39RE Ch. 24 - Prob. 40RE Ch. 24 - Prob. 41RE Ch. 24 - Prob. 42RE Ch. 24 - Prob. 43RE Ch. 24 - Prob. 44RE Ch. 24 - Prob. 45RE Ch. 24 - Prob. 46RE Ch. 24 - Prob. 47RE Ch. 24 - Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - Prob. 87RE Ch. 24 - Prob. 88RE Ch. 24 - Prob. 89RE Ch. 24 - Prob. 90RE Ch. 24 - Prob. 91RE Ch. 24 - Prob. 92RE Ch. 24 - Prob. 93RE Ch. 24 - Prob. 94RE Ch. 24 - Prob. 95RE Ch. 24 - Prob. 1PT Ch. 24 - Prob. 2PT Ch. 24 - Prob. 3PT Ch. 24 - Prob. 4PT Ch. 24 - Prob. 5PT Ch. 24 - Prob. 6PT Ch. 24 - Prob. 7PT Ch. 24 - Prob. 8PT Ch. 24 - Prob. 9PT Ch. 24 - Prob. 10PT

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