Math 1161 – Quiz 8, due 4/3/09
Name
1. You have been hired as a consultant by a farmer who needs to build a grain silo. The
silo is to have the shape of a cylinder, with a roof in the shape of a half–sphere. The
silo must have a total volume of 2400πcubic feet. Your job is to inform the farmer of
the dimensions of the silo that will minimize the total cost of materials. The material
for the side (the cylindrical part) costs $1.50 per square foot, and the material for the
roof (the half–sphere) costs $5 per square foot.
Your answer to this question should include: The set-up and equations you used to
solve the problem; the values of rand hthat minimize the cost, and the total cost for
the materials. Give your answers correct to two decimal places. You can write on the
back if you need more space. Please be neat.