Problem 4P

A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base. a Determine a way to slice the water into parallel rectangular cross-sections and then set up a definite integral for the volume of the water in the glass. b Determine a way to slice the water into parallel cross-sections that are trapezoids and then set up a definite integral for the volume of the water. c Find the volume of water in the glass by evaluating one of the integrals in part a or part b. d Find the volume of the water in the glass from purely geometric considerations. e Suppose the glass is tilted until the water exactly covers half the base. In what direction can you slice the water into triangular cross-sections? Rectangular cross-sections? Cross-sections that are segments of circles? Find the volume of water in the glass.

Step-by-Step Solution