The dimensions of minimize surface area are and the minimum surface area is
Further explanation:
Given:
The volume of the rectangular box is
Explanation:
Consider the base length of the square box as “x”.
Consider the height of the box as “y”.
The surface area of the open box can be expressed as follows,
The volume of the box is
The surface area of the box can be expressed as,
Differentiate the surface area with respect to “x”.
Substitute 0 for in above equation to obtain the value of x.
Further solve the above equation.
The side of the base is
The height of the box can be obtained as follows,
The height of the box is
The surface area of the box can be calculated as follows,
The dimensions of minimize surface area are and the minimum surface area is
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Application of Derivatives
Keywords: Drum, tight containers, open top, square base, volume of 62.5 inches cubed, rectangular box, minimum surface area, dimensions, designing.