Rog_Sec_14_1_P_2

Rog_Sec_14_1_P_2 - (8/15/08) Math 20C. Lecture Examples....

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Math 20C. Lecture Examples. Section 14.1, Part 2. Functions of three or more variables Example 1 The frustum of a right circular cone with base of radius R (meters), top of radius r (meters), and height h (meters) (Figure 1) has volume V ( R,r, h ) = 1 3 π ( R 2 + rR + r 2 ) h . (a) What are the domain and range of V ? (b) What does V (6 , 4 , 9) represent and what is its value if lengths are measured in meters? (b) What is the geometric interpretation of V ( R, 0 , h )? FIGURE 1 Answer: (a) The domain of V consists of all points ( R, r, h ) in three-dimensional Rrh -space such that R 0 , r 0 , h 0. Its range is the interval [0 , ) on a V -axis. (b) V (9 , 6 , 4) is the volume of a frustum of a right circular cone with base of radius 9 meters, top of radius 6 meters, and 4 meters high. V (9 , 6 , 4) = 228 π cubic meters (c) V ( R, 0 ,h ) = 1 3 πR 2 h is the volume of a right circular cone whose base has radius R and whose height is h . (Figure A1) Figure A1 Lecture notes to accompany Section 14.1, Part 2 of Calculus, Early Transcendentals by Rogawski. 1
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This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

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Rog_Sec_14_1_P_2 - (8/15/08) Math 20C. Lecture Examples....

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