Designing a box Two squares of length x are cut out of adjacentcorners of an 18" x 18" piece of cardboard and two rectangles oflength 9" and width x are cut out of the other two corners of thecardboard (see figure). The resulting piece of cardboard is thenfolded along the dashed lines to form an enclosed box. Find thedimensions and volume of the largest box that can be formed in this way.
Designing a box Two squares of length x are cut out of adjacentcorners of an 18" x 18" piece of cardboard and two rectangles oflength 9" and width x are cut out of the other two corners of thecardboard (see figure). The resulting piece of cardboard is thenfolded along the dashed lines to form an enclosed box. Find thedimensions and volume of the largest box that can be formed in this way.
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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Designing a box Two squares of length x are cut out of adjacent
corners of an 18" x 18" piece of cardboard and two rectangles of
length 9" and width x are cut out of the other two corners of the
cardboard (see figure). The resulting piece of cardboard is then
folded along the dashed lines to form an enclosed box. Find the
dimensions and volume of the largest box that can be formed in this way.
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Step 1: Given
VIEWStep 2: Find the dimensions of rectangular box
VIEWStep 3: Substitute the values of L, W and H into formula of volume of a rectangular box
VIEWStep 4: : Find V’
VIEWStep 5: Find at what value of x, V’=0
VIEWStep 6: Now try the solutions by plugging into V
VIEWStep 7: Use x=3 to find L and W
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