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A box is to be made out of a 10 cm by 20 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) Express the volume V of the box as a function of x. cm3 (b) Give the domain of V in interval notation. (Use the fact that length, width and volume must be positive.) (c) Find the length L, width W , and height H of the resulting box that maximizes the volume. (Assume that W < L). L = cm cm Н- cm (d) The maximum volume of the box is cm³.

A box is to be made out of a 10 cm by 20 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) Express the volume V of the box as a function of x. cm3 (b) Give the domain of V in interval notation. (Use the fact that length, width and volume must be positive.) (c) Find the length L, width W , and height H of the resulting box that maximizes the volume. (Assume that W < L). L = cm cm Н- cm (d) The maximum volume of the box is cm³.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.1: Multiplication Properties Of Exponents
Problem 4AGP
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A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length x cm will be cut out of
Transcribed Image Text:A box is to be made out of a 10 cm by 20 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) Express the volume V of the box as a function of x. cm3 (b) Give the domain of V in interval notation. (Use the fact that length, width and volume must be positive.) (c) Find the length L, width W , and height H of the resulting box that maximizes the volume. (Assume that W < L). L = cm cm Н- cm (d) The maximum volume of the box is cm³.
Transcribed Image Text:each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of x. cm3 (b) Give the domain of V in interval notation. (Use the fact that length, width and volume must be positive.) (c) Find the length L, width W , and height H of the resulting box that maximizes the volume. (Assume that W < L). L = cm cm Н- cm (d) The maximum volume of the box is cm³.
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