Optimizing the Surface Area of a Closed Cylinder
A manufacturer wishes to design a closed cylindrical can (with both a top and a bottom) having a fixed volume \(V\) (in cubic units). The surface area of the can is given by \(S = 2\pi r^2 + 2\pi r h\), where \(r\) is the radius and \(h\) is the height. Using the volume constraint […]
Optimizing Dimensions of a Composite Water Tank with Trigonometric Constraint
A company wants to design a closed water tank that consists of a right circular cylinder with a hemispherical top. The cylinder has a radius \(r\) and a height \(h\), and the hemispherical top has the same radius \(r\). To introduce a design twist, the height \(h\) of the cylinder is determined by a trigonometric […]