Maximum Volume A rectangular solid with a square base has a surface area of 337.5square centimeters.(a) Determine the dimensions that yield the maximum volume.(b) Find the maximum volume.check_circle Expert Solution(a)To determineTo calculate: The dimension of the rectangular solid with a square base that yield themaximum volume.Answer to Problem 8EThe dimension of the rectangular solid is Explanation of Solution Find launch 7.5cm × 7.5cm × 7.5cm Given Information:The surface area of the rectangular solid is337.5 sq.cm.Formula used: Volume of the rectangular solid:V = x y2 And the surface area of the rectangular solid is,S = 2x + 4xy2 Where ‘x’ is the length of the square base and ‘y’ is the breadth of the rectangular solid. The following procedure are used for optimization of function. Step 1: Write primary equation for quantity that to be optimization.Step 2: Reduce the primary equation to one single variable with help of secondary equation.Step 3: Find first derivative and set equal to zero to determine critical point. Calculation: As given, the surface area of the rectangular solid is 337.5 sq.cmFormula of area of rectangular solid:S = 2x + 4xy2. Thus,2x + 4xy = 337.5 y =337.5−2x2/4 As, volume of the rectangular solid:V = x y2 Substitute in above:y =337.5−2x24x V = ( x2337.5−2x24x=337.5x−2x34 Differentiate both sides the function with respect to x. dVdxdd x337.5x−2x34= −dVdx337.543x22
Maximum Volume A rectangular solid with a square base has a surface area of 337.5square centimeters.(a) Determine the dimensions that yield the maximum volume.(b) Find the maximum volume.check_circle Expert Solution(a)To determineTo calculate: The dimension of the rectangular solid with a square base that yield themaximum volume.Answer to Problem 8EThe dimension of the rectangular solid is Explanation of Solution Find launch 7.5cm × 7.5cm × 7.5cm Given Information:The surface area of the rectangular solid is337.5 sq.cm.Formula used: Volume of the rectangular solid:V = x y2 And the surface area of the rectangular solid is,S = 2x + 4xy
2 Where ‘x’ is the length of the square base and ‘y’ is the breadth of the rectangular solid. The following procedure are used for optimization of function. Step 1: Write primary equation for quantity that to be optimization.Step 2: Reduce the primary equation to one single variable with help of secondary equation.Step 3: Find first derivative and set equal to zero to determine critical point. Calculation: As given, the surface area of the rectangular solid is 337.5 sq.cmFormula of area of rectangular solid:S = 2x + 4xy2. Thus,2x + 4xy = 337.5 y =337.5−2x2/4 As, volume of the rectangular solid:V = x y2 Substitute in above:y =337.5−2x24x V = ( x2337.5−2x24x=337.5x−2x34 Differentiate both sides the function with respect to x. dVdxdd x337.5x−2x34= −dVdx337.543x22
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