Chapter 7 Practice Sheet

# Chapter 7 Practice Sheet - It is filled with alcohol of...

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Calculus II – Chapter 6 Practice Sheet Name _________________________________ 1. A spring has a natural length of 2 ft, and a force of 15 lb is required to hold it compressed at a length of 18 in. How much work is done in stretching this spring from its natural length to a length of 3 ft? 2. A conical tank is upended so that its vertex is at ground level and its axis is vertical. The tank has radius 5 ft and its height is 10 ft. Compute the work done in filling this tank with water pumped in from ground level. 3. Consider a spherical water tank whose radius is 10 ft and whose center is 50 ft above the ground. How much work is required to fill this tank by pumping water up from ground level? (Suggestion: It may simplify your computations to take y=0 at the center of the tank and to think of the distance each horizontal slice of water must be lifted.) 4. A tank in the shape of a hemisphere of radius 60 is resting on its flat base with the curved surface on top.
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Unformatted text preview: It is filled with alcohol of density 40 lb/ft 3 . How much work is done in pumping all the alcohol to the level of the top of the tank? 5. Find the surface area of revolution generated by rotating the region bounded by 2 x x y-= , = x , and 1 = x , around the x-axis. 6. Find the length of the smooth arc from x = 0 to x = 2 on the curve ( 29 2 / 3 2 1 3 2 + = x y . 7. Find the volume of the solid generated by rotating around the indicated axis the region bounded by the given curves. a. axis x y y x y x-= = + = ; , 3 2 , b. ; 2 , , 3 = = = x y x y about the line x = 3 c. axis y x x y e y x-= = = =-; 1 , , , 2 d. axis x x x y e y x-= = = = ; 1 , , , e. ; 8 , 2 2 x y x y-= = the line y = -1 f. ; 4 , 2 x y x y = = the line x = 5 8. Find the area of the region bounded between the given curves. a. x y x y 2 , 2 = = b. x y x y-= = 8 , 2 1 2...
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## This note was uploaded on 01/13/2012 for the course MATH 2564 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

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