Skip to main content

High School Math Calculus Precalculus with Limits: A Graphing Approach

The volume of the parallelepiped at right with given vertices A ( 0 , 0 , 5 ) , B ( 0 , 10 , 5 ) , C ( 4 , 10 , 5 ) , D ( 4 , 0 , 5 ) , E ( 0 , 1 , 0 ) , F ( 0 , 11 , 0 ) , G ( 4 , 11 , 0 ) and H ( 4 , 1 , 0 ) .

The volume of the parallelepiped at right with given vertices A ( 0 , 0 , 5 ) , B ( 0 , 10 , 5 ) , C ( 4 , 10 , 5 ) , D ( 4 , 0 , 5 ) , E ( 0 , 1 , 0 ) , F ( 0 , 11 , 0 ) , G ( 4 , 11 , 0 ) and H ( 4 , 1 , 0 ) .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

See similar textbooks

Videos

Question

Chapter 10, Problem 16CT

To determine

To find: The volume of the parallelepiped at right with given vertices A(0,0,5) , B(0,10,5) , C(4,10,5) , D(4,0,5) , E(0,1,0) , F(0,11,0) , G(4,11,0) and H(4,1,0) .

Expert Solution & Answer

Answer to Problem 16CT

The volume of the parallelepiped at right with given vertices A(0,0,5) , B(0,10,5) , C(4,10,5) , D(4,0,5) , E(0,1,0) , F(0,11,0) , G(4,11,0) and H(4,1,0) is 200 .

Explanation of Solution

Given information:

The vertices of the parallelepiped are A(0,0,5) , B(0,10,5) , C(4,10,5) , D(4,0,5) , E(0,1,0) , F(0,11,0) , G(4,11,0) and H(4,1,0) .

Precalculus with Limits: A Graphing Approach, Chapter 10, Problem 16CT

Calculation:

First find the vector of length of the parallelepiped AB .

AB=(0−0)i+(10−0)j+(5−5)k=10j

Now find the vector of breadth of the parallelepiped AD .

AD=(4−0)i+(0−0)j+(5−5)k=4i

Now find the vector of height of the parallelepiped AE .

AE=(0−0)i+(1−0)j+(0−5)k=j−5k

Use the formula for triple scalar product for volume of parallelepiped.

AB⋅(AD×AE)=|010040001−5|=0(−5×0−1×0)−10(−5×4−0×0)+0(4×1−0×0)=0−10(−20)+0=200

Therefore, the volume of the parallelepiped at right with given vertices A(0,0,5) , B(0,10,5) , C(4,10,5) , D(4,0,5) , E(0,1,0) , F(0,11,0) , G(4,11,0) and H(4,1,0) is 200 .

Chapter 10, Problem 15CT

Chapter 10, Problem 17CT

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Prob. 62E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 64E Ch. 10.1 - Prob. 65E Ch. 10.1 - Prob. 66E Ch. 10.1 - Prob. 67E Ch. 10.1 - Prob. 68E Ch. 10.1 - Prob. 69E Ch. 10.1 - Prob. 70E Ch. 10.1 - Prob. 71E Ch. 10.1 - Prob. 72E Ch. 10.1 - Prob. 73E Ch. 10.1 - Prob. 74E Ch. 10.1 - Prob. 75E Ch. 10.1 - Prob. 76E Ch. 10.1 - Prob. 77E Ch. 10.1 - Prob. 78E Ch. 10.1 - Prob. 79E Ch. 10.1 - Prob. 80E Ch. 10.1 - Prob. 81E Ch. 10.1 - Prob. 82E Ch. 10.1 - Prob. 83E Ch. 10.1 - Prob. 84E Ch. 10.1 - Prob. 85E Ch. 10.1 - Prob. 86E Ch. 10.1 - Prob. 87E Ch. 10.1 - Prob. 88E Ch. 10.1 - Prob. 89E Ch. 10.1 - Prob. 90E Ch. 10.1 - Prob. 91E Ch. 10.1 - Prob. 92E Ch. 10.1 - Prob. 93E Ch. 10.1 - Prob. 94E Ch. 10.1 - Prob. 95E Ch. 10.1 - Prob. 96E Ch. 10.1 - Prob. 97E Ch. 10.1 - Prob. 98E Ch. 10.1 - Prob. 99E Ch. 10.1 - Prob. 100E Ch. 10.1 - Prob. 101E Ch. 10.1 - Prob. 102E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - Prob. 37E Ch. 10.2 - Prob. 38E Ch. 10.2 - Prob. 39E Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - Prob. 42E Ch. 10.2 - Prob. 43E Ch. 10.2 - Prob. 44E Ch. 10.2 - Prob. 45E Ch. 10.2 - Prob. 46E Ch. 10.2 - Prob. 47E Ch. 10.2 - Prob. 48E Ch. 10.2 - Prob. 49E Ch. 10.2 - Prob. 50E Ch. 10.2 - Prob. 51E Ch. 10.2 - Prob. 52E Ch. 10.2 - Prob. 53E Ch. 10.2 - Prob. 54E Ch. 10.2 - Prob. 55E Ch. 10.2 - Prob. 56E Ch. 10.2 - Prob. 57E Ch. 10.2 - Prob. 58E Ch. 10.2 - Prob. 59E Ch. 10.2 - Prob. 60E Ch. 10.2 - Prob. 61E Ch. 10.2 - Prob. 62E Ch. 10.2 - Prob. 63E Ch. 10.2 - Prob. 64E Ch. 10.2 - Prob. 65E Ch. 10.2 - Prob. 66E Ch. 10.2 - Prob. 67E Ch. 10.2 - Prob. 68E Ch. 10.2 - Prob. 69E Ch. 10.2 - Prob. 70E Ch. 10.2 - Prob. 71E Ch. 10.2 - Prob. 72E Ch. 10.2 - Prob. 73E Ch. 10.2 - Prob. 74E Ch. 10.2 - Prob. 75E Ch. 10.2 - Prob. 76E Ch. 10.2 - Prob. 77E Ch. 10.2 - Prob. 78E Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 45E Ch. 10.3 - Prob. 46E Ch. 10.3 - Prob. 47E Ch. 10.3 - Prob. 48E Ch. 10.3 - Prob. 49E Ch. 10.3 - Prob. 50E Ch. 10.3 - Prob. 51E Ch. 10.3 - Prob. 52E Ch. 10.3 - Prob. 53E Ch. 10.3 - Prob. 54E Ch. 10.3 - Prob. 55E Ch. 10.3 - Prob. 56E Ch. 10.3 - Prob. 57E Ch. 10.3 - Prob. 58E Ch. 10.3 - Prob. 59E Ch. 10.3 - Prob. 60E Ch. 10.3 - Prob. 61E Ch. 10.3 - Prob. 62E Ch. 10.3 - Prob. 63E Ch. 10.3 - Prob. 64E Ch. 10.3 - Prob. 65E Ch. 10.3 - Prob. 66E Ch. 10.3 - Prob. 67E Ch. 10.3 - Prob. 68E Ch. 10.3 - Prob. 69E Ch. 10.3 - Prob. 70E Ch. 10.3 - Prob. 71E Ch. 10.3 - Prob. 72E Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Prob. 34E Ch. 10.4 - Prob. 35E Ch. 10.4 - Prob. 36E Ch. 10.4 - Prob. 37E Ch. 10.4 - Prob. 38E Ch. 10.4 - Prob. 39E Ch. 10.4 - Prob. 40E Ch. 10.4 - Prob. 41E Ch. 10.4 - Prob. 42E Ch. 10.4 - Prob. 43E Ch. 10.4 - Prob. 44E Ch. 10.4 - Prob. 45E Ch. 10.4 - Prob. 46E Ch. 10.4 - Prob. 47E Ch. 10.4 - Prob. 48E Ch. 10.4 - Prob. 49E Ch. 10.4 - Prob. 50E Ch. 10.4 - Prob. 51E Ch. 10.4 - Prob. 52E Ch. 10.4 - Prob. 53E Ch. 10.4 - Prob. 54E Ch. 10.4 - Prob. 55E Ch. 10.4 - Prob. 56E Ch. 10.4 - Prob. 57E Ch. 10.4 - Prob. 58E Ch. 10.4 - Prob. 59E Ch. 10.4 - Prob. 60E Ch. 10.4 - Prob. 61E Ch. 10.4 - Prob. 62E Ch. 10.4 - Prob. 63E Ch. 10.4 - Prob. 64E Ch. 10.4 - Prob. 65E Ch. 10.4 - Prob. 66E Ch. 10.4 - Prob. 67E Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - Prob. 20RE Ch. 10 - Prob. 21RE Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - Prob. 26RE Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Prob. 29RE Ch. 10 - Prob. 30RE Ch. 10 - Prob. 31RE Ch. 10 - Prob. 32RE Ch. 10 - Prob. 33RE Ch. 10 - Prob. 34RE Ch. 10 - Prob. 35RE Ch. 10 - Prob. 36RE Ch. 10 - Prob. 37RE Ch. 10 - Prob. 38RE Ch. 10 - Prob. 39RE Ch. 10 - Prob. 40RE Ch. 10 - Prob. 41RE Ch. 10 - Prob. 42RE Ch. 10 - Prob. 43RE Ch. 10 - Prob. 44RE Ch. 10 - Prob. 45RE Ch. 10 - Prob. 46RE Ch. 10 - Prob. 47RE Ch. 10 - Prob. 48RE Ch. 10 - Prob. 49RE Ch. 10 - Prob. 50RE Ch. 10 - Prob. 51RE Ch. 10 - Prob. 52RE Ch. 10 - Prob. 53RE Ch. 10 - Prob. 54RE Ch. 10 - Prob. 55RE Ch. 10 - Prob. 56RE Ch. 10 - Prob. 57RE Ch. 10 - Prob. 58RE Ch. 10 - Prob. 59RE Ch. 10 - Prob. 60RE Ch. 10 - Prob. 61RE Ch. 10 - Prob. 62RE Ch. 10 - Prob. 63RE Ch. 10 - Prob. 64RE Ch. 10 - Prob. 65RE Ch. 10 - Prob. 66RE Ch. 10 - Prob. 67RE Ch. 10 - Prob. 68RE Ch. 10 - Prob. 69RE Ch. 10 - Prob. 70RE Ch. 10 - Prob. 71RE Ch. 10 - Prob. 72RE Ch. 10 - Prob. 73RE Ch. 10 - Prob. 74RE Ch. 10 - Prob. 75RE Ch. 10 - Prob. 76RE Ch. 10 - Prob. 77RE Ch. 10 - Prob. 78RE Ch. 10 - Prob. 1CT Ch. 10 - Prob. 2CT Ch. 10 - Prob. 3CT Ch. 10 - Prob. 4CT Ch. 10 - Prob. 5CT Ch. 10 - Prob. 6CT Ch. 10 - Prob. 7CT Ch. 10 - Prob. 8CT Ch. 10 - Prob. 9CT Ch. 10 - Prob. 10CT Ch. 10 - Prob. 11CT Ch. 10 - Prob. 12CT Ch. 10 - Prob. 13CT Ch. 10 - Prob. 14CT Ch. 10 - Prob. 15CT Ch. 10 - Prob. 16CT Ch. 10 - Prob. 17CT Ch. 10 - Prob. 18CT Ch. 10 - Prob. 19CT

Knowledge Booster

Background pattern image

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning

Text book image

Calculus: Early Transcendentals

Calculus

ISBN:9781285741550

Author:James Stewart

Publisher:Cengage Learning

Text book image

Thomas' Calculus (14th Edition)

Calculus

ISBN:9780134438986

Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:PEARSON

Text book image

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:9780134763644

Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:PEARSON

Text book image

Calculus: Early Transcendentals

Calculus

ISBN:9781319050740

Author:Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:W. H. Freeman

Text book image

Calculus

ISBN:9780135189405

Author:Michael Sullivan

Publisher:PEARSON

Text book image

Calculus: Early Transcendental Functions

Calculus

ISBN:9781337552516

Author:Ron Larson, Bruce H. Edwards

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Inner Product Spaces; Author: Jeff Suzuki: The Random Professor;https://www.youtube.com/watch?v=JzCZUx9ZTe8;License: Standard YouTube License, CC-BY