Supplemental Instruction
Iowa State University / Leader: / Rosalie Dubberke
Course: / Math 166
Instructor: / Johnston
Date:
Directions
Okay guys, here’s the deal. You’ve got an exam this Friday and I want you all to do great, so I’ve prepared some questions to get a little practice in before you take the test. This is the worksheet you can print out and bring if you want to be able to have the questions in front of you. They (should be) numbered the same as the questions on the slides I’ll be presenting. We are going to go through as many of the questions as possible, but we might skip around. Also, I can’t believe you read this far into the directions, congratulations you deserve a high five. Maybe get one from your neighbor.
Exercises:
1)A solid lies between planes perpendicular to the x-axis at x = -1 and x = 1. The cross-sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = to the parabola y = 2-
Solve for the volume of the solid
2)The base of the solid is the disk the cross-sections by planes perpendicular to the y-axis between y = -1 and y = 1 are isosceles right triangle with one leg in the disk.
3)Find the volume of the region in the first quadrant bound by and the x-axis revolved around the y - axis
4)Find an equation for (but do not solve) the volume of the region in the first quadrant bound by and the x-axis revolved around x = -7
5)Write an equation for (but do not solve) the volume of the area below from 0 < x < 8 using:
Shell method
Washer/disk method
6)Write an equation for the volume of the area between and revolved around the line x = 6 using:
Shell method
Washer/disk method
Solve one
7)Find the length of the curve from 0 < x < 1
8)Find the surface area of the equation revolved around the x-axis from x = 1 to x = 2
9)Find the surface area of the equation x = 1 - y revolved around the y-axis from 0 to 1
10)A cable that weighs 2lbs/ft is attached to a bucket filled with coal that weighs 800 lbs. The bucket is initially at the bottom of a 500 ft mine shaft. Answer each of the following questions:
Determine the amount of work required to lift the bucket to the midpoint of the shaft.
Determine the amount of work required to lift the bucket from the midpoint of the shaft to the top.
Determine the amount of work required to life the bucket all the way to the top of the shaft.
11)A cylindrical; reservoir diameter 4 ft and height 6 ft is half full of water weighing . Find the work done in emptying the water over the top.
12)A cylindrical; reservoir diameter 4 ft and height 6 ft is half full of water weighing . Write an equation for the work done in emptying the water 3 feet over the top.
13)A force of 1200 N compresses a spring from its natural length of 18 cm to a length of 16 cm. How much work is done in compressing it from 16 cm to 14 cm?
14)A leaky bucket weighing 5N is lifted 20 m into the air at a constant speed. The rope weighs 0.08 Nm-1. The bucket starts with 2 N of water and leaks at a constant rate. It finishes draining just as it reaches the top. How much work was done lifting the bucket, the water, and the rope?
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