Eksplorasi Masalah Isoperimetrik pada Bangun Ruang
Abstract
In two-dimensional figures, the isoperimetric problem is defined as finding two-dimensional figures that will produce the largest area among several two-dimensional figures with the same perimeter. In this research, the isoperimetric problem is extended to find the shape with the largest volume among the shapes that have the same surface area. The aim of this research is to solve isoperimetric problems in three-dimensional shapes obtained by comparing various shapes of three-dimensional shapes. The discussion in this research is limited to three-dimensional shapes in the form of prisms with regular n-sided bases, pyramids with regular n-sided bases, cylinders, cones, and spheres. This research method uses concepts from calculus, trigonometry and algebra to prove the isoperimetric theorem with a simple and elementary approach. The result of this research is that the order of the maximum volume of three-dimensional shapes if the surface area is the same from smallest to largest is a pyramid with an equilateral triangular base, a pyramid with a square base, a prism with an equilateral triangular base, a pyramid with a regular n-sided base (n≥5), cone, prism with square base, prism with regular n-sided base (n≥5), cylinder, and sphere.
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DOI: https://doi.org/10.37905/euler.v12i1.24918
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