1. A large tank is designed with ends in the shape of the region between the curves {image} and {image} , measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of 7 ft with gasoline. (Assume the gasoline's density is {image} .)
5,030 lb
4,942 lb
5,177 lb
5,044 lb
5,114 lb
5,109 lb 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The masses {image} and {image} are located at the points {image} and {image} . True or False: The center of mass of the system is {image} .
True
False 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Find the centroid of the region bounded by the curves. {image}1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. True or False: The center of mass of a lamina with density {image} in the shape of a circle with radius 9 as shown below is {image} . {applet}
True
False 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Use the Theorem of Pappus to find the volume of the given solid
Use the Theorem of Pappus to find the volume of the given solid. The solid obtained by rotating the triangle with vertices ( 2, 2 ), ( 2, 6 ), and ( 6, 4 ) about the x - axis.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50