Teacher's graded activity

Suppose the town of Cambridge wants to repaint its water tower for the upcoming centennial celebration. Plans call for a brand of paint that is very durable, but VERY expensive. You have been hired by the Mayor's Office to determine how much paint will be needed for the job.

From the original engineering blueprints, you see that the tower is a solid of revolution with three distinct parts.

The Onion - defined by the region enclosed by the graph of x = 12+ Vy (50- y) from 40 Y = 0 to y = 50 revolved about the y-axis. The Tube - a cylinder of height 40 feet and radius 12 feet The Trumpet - a truncated cone, 30 feet tall, with a base diameter of 40 feet