Answer:
Radius =6.518 feet
Height = 26.074 feet
Step-by-step explanation:
The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder
Volume of a Hemisphere
Volume of a Cylinder
Therefore:
The Volume of the Solid formed
Area of the Hemisphere =
Curved Surface Area of the Cylinder =
Total Surface Area=
Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.
Therefore total Cost, C
Recall:
Therefore:
The minimum cost occurs at the point where the derivative equals zero.
Recall:
Therefore, the dimensions that will minimize the cost are:
Radius =6.518 feet
Height = 26.074 feet