A grain storage silo with a filling opening on the very top is designed to have a volume of 576π cubic yards. It has a cylindrical shape with a hemisphere on the top and needs no base. Note that the...

A grain storage silo with a filling opening on the very top is designed to have a volume of 576π cubic yards. It has a cylindrical shape with a hemisphere on the top and needs no base. Note that the hemispherical top can also be filled completely. If the hemispherical top requires material that is $10 per square yard and the cylindrical side needs material that is $5 per square yard, determine the dimensions that will minimize the total cost. Also find the cost of the optimum silo to the nearest dollar.