A square based box is to be constructed such that its volume is exactly 1.8m³. The following questions guide you through the process of determining the base side length and box height such that the minimum amount of cardboard is used to construct the box. a) The equation for box volume can be used to express box height in terms of the side length of the bas of the box. If the side length is denoted x, enter the function here b) Use your result from part (a) to write a function for the surface area of cardboard used in the construction of the box. Your function should be entirely in terms of the side length of the base of the box, x.
A square based box is to be constructed such that its volume is exactly 1.8m³. The following questions guide you through the process of determining the base side length and box height such that the minimum amount of cardboard is used to construct the box. a) The equation for box volume can be used to express box height in terms of the side length of the bas of the box. If the side length is denoted x, enter the function here b) Use your result from part (a) to write a function for the surface area of cardboard used in the construction of the box. Your function should be entirely in terms of the side length of the base of the box, x.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:To minimise the surface area of cardboard, we need the derivative of the surface area function with respect to . This derivative is
ds
dz
d)
The minimum surface area will occur when the length of the sides of the box base is =
e)
Finally, the height of the box must then be h =
||
Transcribed Image Text:A square based box is to be constructed such that its volume is exactly 1.8m³. The following questions
guide you through the process of determining the base side length and box height such that the
minimum amount of cardboard is used to construct the box.
a)
The equation for box volume can be used to express box height in terms of the side length of the bas
of the box. If the side length is denoted x, enter the function here
b)
Use your result from part (a) to write a function for the surface area of cardboard used in the
construction of the box. Your function should be entirely in terms of the side length of the base of the
box, x.
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answer the tow atteched question that are part of thge previous question and alos the last answer (c) you gave was incorrect plseae check .thanks
Transcribed Image Text:d)
The minimum surface area will occur when the length of the sides of the box base is a
=
e)
Finally, the height of the box must then be h
=
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