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 5 ft with gasoline. (Assume the gasoline's density is {image} .)
2,248 lb
2,253 lb
2,169 lb
2,183 lb
2,081 lb
2,316 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.
{image} 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 21 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 ( 5, 3 ), ( 5, 9 ), and ( 10, 6 ) 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