Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
e value of alpha(angle) is 40 degre

e value of alpha(angle) is 40 degre

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 36E
See similar textbooks
icon
Related questions
Question

the value of alpha(angle) is 40 degree

A designer proposed using a paraboloid S: x² + y? = z as the basis of a container design. However, after some discussion, the designer was advised to revert to a matching cone-based design S, with certain apex angle a, which was said to be able to achieve material cost saving due to less surface area. Figure 1 gives a visual comparison of the two surfaces. 12 14 radius 0.8 0.6 S2: Cone 04 apex langle a S1: Paraboloid x + y² = z 02 -12 --0.8 -0.6 -0.4 -0.2 04 0.6 08 12 Figure 1: Visual representations* of the paraboloid surface and its matching cone surface *Note: the graphs are for illustrative purpose only; the intersection between S, and S, depends on a and does not always occur at z = 1
Transcribed Image Text:A designer proposed using a paraboloid S: x² + y? = z as the basis of a container design. However, after some discussion, the designer was advised to revert to a matching cone-based design S, with certain apex angle a, which was said to be able to achieve material cost saving due to less surface area. Figure 1 gives a visual comparison of the two surfaces. 12 14 radius 0.8 0.6 S2: Cone 04 apex langle a S1: Paraboloid x + y² = z 02 -12 --0.8 -0.6 -0.4 -0.2 04 0.6 08 12 Figure 1: Visual representations* of the paraboloid surface and its matching cone surface *Note: the graphs are for illustrative purpose only; the intersection between S, and S, depends on a and does not always occur at z = 1
With your knowledge in surface integral**, determine the surface area of the cone (S2) and the surface area of the paraboloid (S,), and find out the surface area saving. Be sure to refer Table 1 for the value of the apex angle a. Digit a (*) 4 40 **Note: it is recommended to use suitable parameterization for ease of evaluating the two surface integrals: e.g. a possible approach is to view the cone as a circular revolution of a slanted line around the central-axis, so that for every elevation value z, the x and y are related by the basic circular equation x² + y² = (radius)² (see Figure 1). This revolution approach is applicable to the paraboloid as well. END
Transcribed Image Text:With your knowledge in surface integral**, determine the surface area of the cone (S2) and the surface area of the paraboloid (S,), and find out the surface area saving. Be sure to refer Table 1 for the value of the apex angle a. Digit a (*) 4 40 **Note: it is recommended to use suitable parameterization for ease of evaluating the two surface integrals: e.g. a possible approach is to view the cone as a circular revolution of a slanted line around the central-axis, so that for every elevation value z, the x and y are related by the basic circular equation x² + y² = (radius)² (see Figure 1). This revolution approach is applicable to the paraboloid as well. END
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Types of Angles
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS