21b_ps8 - Co-21B Problem Solving #8T 1) Find the centroid...

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Unformatted text preview: Co-21B Problem Solving #8T 1) Find the centroid of the region bounded by y=1x, y=, x=1and x=2. *Answer: 1ln2,14ln2( )2) Consider the region R bounded by y=1!x2and the x-axis. a) Find the centroid of the region R. *Hint: Use symmetry to find one of the coordinates! *Answer: 0,25( )b) Use Pappuss Theorem to find the volume of the solid formed when R is revolved about the line x= 4. Check your answer using shells 3) Show that the surface area of y=x3,(1!x!2)revolved about the x-axis is the same as y=x, (1!x!8)revolved about the y-axis. b)Then find the area. 4) Find the area of the surface generated by revolving y=2x+1, 1!x!7about the x-axis. 5) Use Pappuss Theorems to find the volume and surface area of the torus formed by revolving x2+(y!5)2=4about the x-axis. 6) Remember that Pappuss Theorem can give you an alternative method to find the centroid of a region: a) Find the volume of the solid formed by revolving the region bounded by y=x2and y=1about the x-axis....
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This note was uploaded on 05/26/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at University of California, Berkeley.

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