Question

A silo​ (base not​ included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction

Answer 1

The dimensions to be used if the volume is fixed at cubic units include:

• Surface area of a cylinder is 2πrh +2πr²

• Volume of cylinder = πr²h

• Volume of a hemisphere = 2/3 π r³

• Surface area of a sphere = 4πr²

What is Volume?

This is defined as the amount of three-dimensional space enclosed by a closed surface.

The dimensions which can be used are shown above where r is radius and h is height.

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