







A volume of revolution 
20080424 

From Sabahat: Hi, i have a region enclosed by both axes, the line x=2 and the curve y=1/8 x2 + 2 is rotated about the yaxis to form a solid . How can i find the volume of this solid?. (Please note that y equation is read as y =1 over 8 times x square plus 2.) I will be really grateful if you answer this question. :) Answered by Harley Weston. 





A volume of revolution 
20060607 

From Colleen: Find the exact volume in cubic units generated by rotating a region, R, around the
yaxis, given that R is the region bounded by the curve y = x^{3} and the lines x = 1 and
y = 8. Answered by Penny Nom. 





A sphere with a hole  cylindrical shells 
20021211 

From Kathy: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters.) You discover that both napkin rings have the same height, h.  Guess which ring has more wood in it and why.
 Check you guess: Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h.
Answered by Penny Nom. 





Catenary 
20020102 

From Jason: I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary. The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the yaxis. Any help you can provide would be greatly appreciated. Answered by Harley Weston. 

