Rog_Sec_14_1_P_2

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online