Hi, I;m having some trouble with the following question: The volume of a box wit

Question

Hi, I;m having some trouble with the following question:The volume of a box with a rectangular base of length 5cmand width of length x cm is 70cm^3. Express the total surface area(A) as a function of the width (x) of the base. I'm not sure exactly how to start this problem and what itmeans to express the total surface area (A) as a function of thewidth (x) of the base. Thanks, Mike Hi, I;m having some trouble with the following question:The volume of a box with a rectangular base of length 5cmand width of length x cm is 70cm^3. Express the total surface area(A) as a function of the width (x) of the base. I'm not sure exactly how to start this problem and what itmeans to express the total surface area (A) as a function of thewidth (x) of the base. Thanks, Mike I'm not sure exactly how to start this problem and what itmeans to express the total surface area (A) as a function of thewidth (x) of the base. Thanks, Mike

Explanation / Answer

the length of the box is 5cm , the width is xcm , let h represent the height of the box. the volume of the box is 70cm^3 . Note that equations comeabout by looking at the same thing in two different ways. the volume is also   V = width( length) (height)   so     70 = 5xh    thus, solving for h weget   h = 14 / x The total surface area is   2(width)(length) + 2(width)(height) + 2(length)(height)                                       = 2(5)(x) + 2(x)(14/x) + 2(5)(14/x)                                        = [ 10x   + 28 + 140/x ] sq.cm hope this helps

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