Chapter72003 - of the tank. 7. A plate has the dimensions...

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Chapter 7 Test February 4, 2003 No Calculators Name Diagrams are recommended but not required. 1. Find the area of the region bounded by the graphs of the equations x y 3 and y x ² 2 and y 2. 2. Find the volume of the solid generated by revolving the region bounded by y 1 ³³³³ 2 x ² 1, y x ² 1, and x 3 about the y ± axis. 3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y x , y x 2 ² 2, and x & 0 ² in the first quadrant ³ about the x ± axis. 4. A solid has as its base the region in the xy ± plane determined by the graphs of the equations x y 2 ² 4 and x 0. Every cross ± section by a plane perpendicular to the y ± axis is a triangle with base equal to height. Find the volume of the solid.
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5. Find the length of the arc for x 2 ±±±± 3 y 3 ² 1 ±±±±±±±± 8 y from y 1 to y 3. 6. A tank in the shape of a cylinder is lying on its side. It has length 6 feet, radius 2 feet, and it is half ³ filled with water. Find the work required to pump all of the water out of the tank to a position 4 feet above the top
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Unformatted text preview: of the tank. 7. A plate has the dimensions of an isoscles trapezoid with base lengths 2 feet and 10 feet, with a height of 4 feet. The plate is submerged in water so that the shortest base is parallel to, and closest to, the surface of the water, at a distance of 5 feet. Find the force exerted on one side of the plate. 8. A force of 12 lbs is required to stretch a spring from its natural length of 5 inches to a length of 8 inches. Find the work done in stretching the spring from a length of 9 inches to a length of 16 inches. 9. Find the volume of the solid generated by revolving the region bounded by y & x 2 2 x and y & x about the line x & 2. 10. Find the volume of the solid generated by revolving the region bounded by x & 4 y y 2 and x & about the line y & 1....
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Chapter72003 - of the tank. 7. A plate has the dimensions...

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