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HH_12_5 - Math 10C Lecture Examples Section 12.5 Functions...

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Unformatted text preview: (10/8/08) Math 10C. Lecture Examples. Section 12.5. Functions of three 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? (c) What is the geometric interpretation of V ( R , , h ) ? FIGURE 1 Answer: (a) The domain of V consists of all points ( R, r, h ) in three-dimensional Rrh-space such that R ≥ , r ≥ , 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, ,h ) = 1 3 πR 2 h is the volume of a right circular cone whose base has radius R and whose height is h ....
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HH_12_5 - Math 10C Lecture Examples Section 12.5 Functions...

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