(a) Explanation Given: The equation of the sphere is: x 2 + y 2 + z 2 = r 2 Formula used: The volume of a solid region when it is revolved about the x -axis using the disk method is: V = ∫ x 1 x 2 π [ R ( x ) ] 2 d x Calculation: Consider the graph of the curve y = r 2 − x 2 , x ≥ 0 shown below. When the curve is revolved about the x -axis, the solid thus obtained is a hemi-sphere with the radius r . Therefore, the volume of sphere using the disk method is, V = 2 π ∫ x 1 x 2 [ R ( x ) ] 2 d x …………………………… (1) The limits for x is: 0 ≤ x ≤ r The equation of the function R ( x ) (b) To determine To calculate: The volume of the ellipsoid x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 .

Calculus: Early Transcendental Functions (MindTap Course List)

6th Edition

ISBN: 9781285774770

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Question

Chapter 11, Problem 8PS

(a)

To determine

To calculate: The volume of the sphere x2+y2+z2=r2 using the disk method.

(b)

To determine

To calculate: The volume of the ellipsoid x2a2+y2b2+z2c2=1.

Expert Solution & Answer

Chapter 11 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 11.1 - Sketching a Vector In Exercises 14, (a) find the...Ch. 11.1 - Sketching a Vector In Exercises 14, (a) find the...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Prob. 10E

Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 27E Ch. 11.1 - Finding a Terminal Point In Exercises 17 and 18,...Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 17E Ch. 11.1 - Sketching Scalar Multiples In Exercises 25 and 26,...Ch. 11.1 - Prob. 19E Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, And the...Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, And the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 57E Ch. 11.1 - Prob. 58E Ch. 11.1 - Prob. 59E Ch. 11.1 - Prob. 60E Ch. 11.1 - Finding Values In Exercises 6166, find aand bsuch...Ch. 11.1 - Prob. 62E Ch. 11.1 - Prob. 63E Ch. 11.1 - Prob. 64E Ch. 11.1 - Prob. 65E Ch. 11.1 - Prob. 66E Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Prob. 68E Ch. 11.1 - Prob. 69E Ch. 11.1 - Prob. 70E Ch. 11.1 - Prob. 71E Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Prob. 73E Ch. 11.1 - Prob. 74E Ch. 11.1 - Prob. 75E Ch. 11.1 - Numerical and Graphical Analysis Forces with...Ch. 11.1 - Prob. 77E Ch. 11.1 - Prob. 78E Ch. 11.1 - Prob. 79E Ch. 11.1 - Cable TensionDetermine the tension in each cable...Ch. 11.1 - Prob. 81E Ch. 11.1 - Prob. 82E Ch. 11.1 - Navigation A plane is flying with a bearing of...Ch. 11.1 - Prob. 84E Ch. 11.1 - Prob. 85E Ch. 11.1 - Prob. 86E Ch. 11.1 - Prob. 87E Ch. 11.1 - True or False? In Exercises 85-94, determine...Ch. 11.1 - Prob. 89E Ch. 11.1 - Prob. 90E Ch. 11.1 - Prob. 91E Ch. 11.1 - Geometry Using vectors, prove that die line...Ch. 11.1 - GeometryUsing vectors, prove that the diagonals of...Ch. 11.1 - Prob. 94E Ch. 11.1 - Prob. 95E Ch. 11.1 - PUTNAM EXAM CHALLENGE A coast artillery gun can...Ch. 11.2 - CONCEPT CHECK Describing Coordinates A point in...Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Finding Coordinates of a Point In Exercises 9-12,...Ch. 11.2 - Finding Coordinates of a Point In Exercises 9-12,...Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Finding the Equation of a Sphere In Exercises...Ch. 11.2 - Finding the Component Form of a Vector in Space In...Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Writing a Vector in Different Forms In Exercises...Ch. 11.2 - Writing a Vector in Different Forms In Exercises...Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Finding a Terminal Point In Exercises 55 and 56,...Ch. 11.2 - Prob. 54E Ch. 11.2 - Finding Scalar Multiples In Exercises 57 and 58,...Ch. 11.2 - Prob. 56E Ch. 11.2 - Prob. 57E Ch. 11.2 - Finding a Vector In Exercises 59-62, find the...Ch. 11.2 - Prob. 59E Ch. 11.2 - Prob. 60E Ch. 11.2 - Prob. 61E Ch. 11.2 - Prob. 62E Ch. 11.2 - Prob. 63E Ch. 11.2 - Prob. 64E Ch. 11.2 - Prob. 65E Ch. 11.2 - Prob. 66E Ch. 11.2 - Prob. 67E Ch. 11.2 - Prob. 68E Ch. 11.2 - Prob. 69E Ch. 11.2 - Prob. 70E Ch. 11.2 - Prob. 71E Ch. 11.2 - Prob. 72E Ch. 11.2 - Prob. 73E Ch. 11.2 - Prob. 74E Ch. 11.2 - Prob. 75E Ch. 11.2 - Prob. 76E Ch. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Prob. 78E Ch. 11.2 - Prob. 79E Ch. 11.2 - Prob. 80E Ch. 11.2 - Prob. 83E Ch. 11.2 - Prob. 84E Ch. 11.2 - Prob. 85E Ch. 11.2 - Prob. 86E Ch. 11.2 - Prob. 87E Ch. 11.2 - Prob. 88E Ch. 11.2 - Prob. 89E Ch. 11.2 - Prob. 90E Ch. 11.2 - Prob. 92E Ch. 11.2 - Prob. 82E Ch. 11.2 - Prob. 81E Ch. 11.2 - Prob. 91E Ch. 11.2 - Prob. 99E Ch. 11.2 - Tower Guy Wire The guy wire supporting a...Ch. 11.2 - Auditorium Lights The lights in an auditorium are...Ch. 11.2 - Think About It Suppose the length of each cable in...Ch. 11.2 - Load Supports Find the tension in each of the...Ch. 11.2 - Prob. 104E Ch. 11.2 - Prob. 105E Ch. 11.2 - Prob. 94E Ch. 11.2 - Prob. 95E Ch. 11.2 - Prob. 96E Ch. 11.2 - Prob. 97E Ch. 11.2 - Prob. 98E Ch. 11.3 - Find (a) u.v (b) u.u (c) (b) (c)(d) (e) v(f)...Ch. 11.3 - Prob. 2E Ch. 11.3 - Find (a) u.v (b) u.u (c) (b) (c)(d) (e) v(f)...Ch. 11.3 - Finding Dot Products In Exercises 18, find (a) u...Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vector In Exercises...Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - The vertices of a triangle are given. Determine...Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Finding Direction Angles In Exercises 31-36, find...Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Finding Direction Angles In Exercises 31-36, find...Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - (a) Find the projection of u onto v and (b) find...Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.3 - When the projection of u onto v has the same...Ch. 11.3 - Prob. 50E Ch. 11.3 - Prob. 51E Ch. 11.3 - Prob. 52E Ch. 11.3 - Prob. 53E Ch. 11.3 - Prob. 54E Ch. 11.3 - Prob. 55E Ch. 11.3 - Prob. 56E Ch. 11.3 - Prob. 57E Ch. 11.3 - Prob. 58E Ch. 11.3 - Prob. 59E Ch. 11.3 - Prob. 60E Ch. 11.3 - Prob. 61E Ch. 11.3 - Prob. 62E Ch. 11.3 - Prob. 63E Ch. 11.3 - Prob. 64E Ch. 11.3 - Prob. 65E Ch. 11.3 - Prob. 66E Ch. 11.3 - In exercise y=x2,y=x1/3 (a) Find all points of...Ch. 11.3 - In exercise y=x3,y=x1/3 (a) Find all points of...Ch. 11.3 - Prob. 69E Ch. 11.3 - Prob. 70E Ch. 11.3 - Prob. 71E Ch. 11.3 - Use vectors to prove that parallelogram is a...Ch. 11.3 - Consider a regular tetrahedron with vertices...Ch. 11.3 - Prob. 74E Ch. 11.3 - Prob. 75E Ch. 11.3 - Prob. 76E Ch. 11.3 - Prob. 77E Ch. 11.3 - Prob. 78E Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Finding Cross Products In Exercises 7-10, find (a)...Ch. 11.4 - Finding Cross Products In Exercises 7-10, find (a)...Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Finding a Cross Product In Exercises 1116, find u...Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Finding a Unit Vector In Exercises 15-18. Find a...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18. Find a...Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Area In Exercises 23 and 24, verify that the...Ch. 11.4 - Area In Exercises 23 and 24, verify that the...Ch. 11.4 - Area In Exercises 25 and 26, find the area of the...Ch. 11.4 - Prob. 28E Ch. 11.4 - Torque The brakes on a bicycle are applied using a...Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Volume In Exercises 35 and 36. use the triple...Ch. 11.4 - Prob. 38E Ch. 11.4 - Volume In Exercises 37 and 38, find the volume of...Ch. 11.4 - Volume In Exercises 37 and 38, find the volume of...Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 53E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Proof In Exercises 47-52. prove the property of...Ch. 11.4 - Prob. 57E Ch. 11.4 - Proof Prove that u(vw)=(uw)v(uv)w Ch. 11.4 - Prob. 59E Ch. 11.5 - CONCEPT CHECK Parametric and Symmetric Equations...Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Prob. 6E Ch. 11.5 - Prob. 7E Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Prob. 28E Ch. 11.5 - Finding a Point of Intersection In Exercises...Ch. 11.5 - Prob. 30E Ch. 11.5 - Prob. 31E Ch. 11.5 - Prob. 32E Ch. 11.5 - Checking Points in a Plane In Exercises 37 and 38,...Ch. 11.5 - Prob. 34E Ch. 11.5 - Prob. 35E Ch. 11.5 - Prob. 36E Ch. 11.5 - Prob. 37E Ch. 11.5 - Prob. 38E Ch. 11.5 - Prob. 39E Ch. 11.5 - Prob. 40E Ch. 11.5 - Prob. 41E Ch. 11.5 - Prob. 42E Ch. 11.5 - Prob. 43E Ch. 11.5 - Prob. 44E Ch. 11.5 - Prob. 45E Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56....Ch. 11.5 - Prob. 47E Ch. 11.5 - Prob. 48E Ch. 11.5 - Prob. 49E Ch. 11.5 - Prob. 50E Ch. 11.5 - Prob. 51E Ch. 11.5 - Prob. 52E Ch. 11.5 - Prob. 53E Ch. 11.5 - Prob. 54E Ch. 11.5 - Prob. 55E Ch. 11.5 - Prob. 56E Ch. 11.5 - Prob. 75E Ch. 11.5 - Prob. 76E Ch. 11.5 - Prob. 57E Ch. 11.5 - Prob. 58E Ch. 11.5 - Prob. 59E Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Prob. 61E Ch. 11.5 - Prob. 62E Ch. 11.5 - Prob. 67E Ch. 11.5 - Prob. 68E Ch. 11.5 - Prob. 63E Ch. 11.5 - Prob. 64E Ch. 11.5 - Prob. 65E Ch. 11.5 - Prob. 66E Ch. 11.5 - Prob. 69E Ch. 11.5 - Prob. 70E Ch. 11.5 - Prob. 71E Ch. 11.5 - Prob. 72E Ch. 11.5 - Prob. 73E Ch. 11.5 - Prob. 74E Ch. 11.5 - Intersection of a Plane and a Line In Exercises...Ch. 11.5 - Prob. 78E Ch. 11.5 - Prob. 79E Ch. 11.5 - Prob. 80E Ch. 11.5 - Prob. 81E Ch. 11.5 - Prob. 82E Ch. 11.5 - Prob. 83E Ch. 11.5 - Prob. 84E Ch. 11.5 - Prob. 85E Ch. 11.5 - Prob. 86E Ch. 11.5 - Prob. 87E Ch. 11.5 - Prob. 88E Ch. 11.5 - Prob. 89E Ch. 11.5 - Prob. 90E Ch. 11.5 - Prob. 91E Ch. 11.5 - Prob. 92E Ch. 11.5 - Prob. 93E Ch. 11.5 - Prob. 94E Ch. 11.5 - Prob. 96E Ch. 11.5 - Prob. 97E Ch. 11.5 - Prob. 98E Ch. 11.5 - Prob. 99E Ch. 11.5 - HOW DO YOU SEE IT? Match the general equation with...Ch. 11.5 - Prob. 101E Ch. 11.5 - Mechanical Design The figure shows a chute at the...Ch. 11.5 - Distance Two insects are crawling along different...Ch. 11.5 - Prob. 104E Ch. 11.5 - Prob. 105E Ch. 11.5 - Prob. 106E Ch. 11.5 - Prob. 107E Ch. 11.5 - Prob. 108E Ch. 11.5 - Prob. 109E Ch. 11.5 - Prob. 110E Ch. 11.5 - Prob. 111E Ch. 11.5 - Prob. 112E Ch. 11.5 - Prob. 113E Ch. 11.5 - Prob. 114E Ch. 11.6 - Prob. 28E Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Prob. 3E Ch. 11.6 - Prob. 4E Ch. 11.6 - Prob. 5E Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Prob. 9E Ch. 11.6 - Prob. 10E Ch. 11.6 - Prob. 11E Ch. 11.6 - Prob. 12E Ch. 11.6 - Prob. 17E Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 20E Ch. 11.6 - Prob. 13E Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 23E Ch. 11.6 - Prob. 22E Ch. 11.6 - Prob. 21E Ch. 11.6 - Prob. 24E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 16E Ch. 11.6 - Prob. 25E Ch. 11.6 - Prob. 26E Ch. 11.6 - Prob. 27E Ch. 11.6 - Prob. 29E Ch. 11.6 - Prob. 30E Ch. 11.6 - Prob. 36E Ch. 11.6 - Prob. 31E Ch. 11.6 - Finding an Equation of a Surface of Revolution In...Ch. 11.6 - Prob. 33E Ch. 11.6 - Prob. 34E Ch. 11.6 - Prob. 35E Ch. 11.6 - Prob. 37E Ch. 11.6 - Prob. 38E Ch. 11.6 - Prob. 39E Ch. 11.6 - Prob. 40E Ch. 11.6 - Prob. 41E Ch. 11.6 - Prob. 42E Ch. 11.6 - Prob. 43E Ch. 11.6 - Finding an Equation of a Surface In Exercises 45...Ch. 11.6 - Geography Because of the forces caused by its...Ch. 11.6 - Machine Design The top of a rubber bushing...Ch. 11.6 - Using a Hyperbolic Paraboloid Determine the...Ch. 11.6 - Prob. 48E Ch. 11.6 - Think About It Three types of classic topological...Ch. 11.6 - Prob. 49E Ch. 11.6 - Prob. 50E Ch. 11.6 - Prob. 51E Ch. 11.6 - Prob. 52E Ch. 11.7 - Prob. 1E Ch. 11.7 - Prob. 2E Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Prob. 5E Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Prob. 15E Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Prob. 17E Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Prob. 20E Ch. 11.7 - Prob. 21E Ch. 11.7 - Prob. 22E Ch. 11.7 - Prob. 23E Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 25E Ch. 11.7 - Prob. 26E Ch. 11.7 - Prob. 27E Ch. 11.7 - Prob. 28E Ch. 11.7 - Prob. 29E Ch. 11.7 - Prob. 30E Ch. 11.7 - Prob. 31E Ch. 11.7 - Prob. 32E Ch. 11.7 - Prob. 33E Ch. 11.7 - Prob. 34E Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Prob. 40E Ch. 11.7 - Prob. 37E Ch. 11.7 - Prob. 38E Ch. 11.7 - Prob. 39E Ch. 11.7 - Prob. 36E Ch. 11.7 - Prob. 41E Ch. 11.7 - Prob. 42E Ch. 11.7 - Prob. 43E Ch. 11.7 - Prob. 44E Ch. 11.7 - Prob. 45E Ch. 11.7 - Prob. 46E Ch. 11.7 - Prob. 47E Ch. 11.7 - Prob. 48E Ch. 11.7 - Prob. 49E Ch. 11.7 - Prob. 50E Ch. 11.7 - Prob. 51E Ch. 11.7 - Prob. 52E Ch. 11.7 - Prob. 53E Ch. 11.7 - Prob. 54E Ch. 11.7 - Prob. 55E Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 63E Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Prob. 68E Ch. 11.7 - Prob. 69E Ch. 11.7 - Prob. 70E Ch. 11.7 - Prob. 71E Ch. 11.7 - Prob. 72E Ch. 11.7 - Prob. 75E Ch. 11.7 - Prob. 76E Ch. 11.7 - Prob. 77E Ch. 11.7 - Prob. 78E Ch. 11.7 - Prob. 57E Ch. 11.7 - Prob. 58E Ch. 11.7 - Prob. 59E Ch. 11.7 - Prob. 60E Ch. 11.7 - Prob. 61E Ch. 11.7 - Prob. 62E Ch. 11.7 - Prob. 80E Ch. 11.7 - Prob. 82E Ch. 11.7 - Prob. 84E Ch. 11.7 - Prob. 85E Ch. 11.7 - Prob. 86E Ch. 11.7 - Prob. 87E Ch. 11.7 - Prob. 65E Ch. 11.7 - Prob. 66E Ch. 11.7 - Prob. 67E Ch. 11.7 - Prob. 73E Ch. 11.7 - Prob. 74E Ch. 11.7 - Prob. 79E Ch. 11.7 - Prob. 81E Ch. 11.7 - Prob. 83E Ch. 11.7 - Prob. 88E Ch. 11.7 - Prob. 89E Ch. 11.7 - Prob. 90E Ch. 11.7 - Prob. 91E Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Prob. 93E Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Prob. 95E Ch. 11.7 - Prob. 96E Ch. 11.7 - Prob. 97E Ch. 11.7 - Prob. 98E Ch. 11.7 - Prob. 99E Ch. 11.7 - Prob. 100E Ch. 11.7 - Prob. 101E Ch. 11.7 - Prob. 102E Ch. 11.7 - Prob. 103E Ch. 11.7 - Prob. 104E Ch. 11.7 - Prob. 105E Ch. 11.7 - Prob. 106E Ch. 11.7 - Prob. 107E Ch. 11.7 - Prob. 108E Ch. 11.7 - Prob. 109E Ch. 11.7 - Prob. 110E Ch. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Torque The specifications for a tractor state that...Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Prob. 57RE Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Prob. 64RE Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Prob. 67RE Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE Ch. 11 - Prob. 74RE Ch. 11 - Prob. 75RE Ch. 11 - Prob. 76RE Ch. 11 - Prob. 77RE Ch. 11 - Prob. 78RE Ch. 11 - Proof Using vectors, prove the Law of Sines: If a,...Ch. 11 - Prob. 2PS Ch. 11 - Prob. 3PS Ch. 11 - Prob. 4PS Ch. 11 - Prob. 5PS Ch. 11 - Prob. 6PS Ch. 11 - Volume (a) Find the volume of the solid bounded...Ch. 11 - Prob. 8PS Ch. 11 - Prob. 9PS Ch. 11 - Prob. 10PS Ch. 11 - Prob. 11PS Ch. 11 - Prob. 12PS Ch. 11 - Tetherball A tetherball weighing 1 pound is pulled...Ch. 11 - Prob. 14PS Ch. 11 - Prob. 15PS Ch. 11 - Prob. 16PS Ch. 11 - Prob. 17PS Ch. 11 - Prob. 18PS Ch. 11 - Prob. 19PS Ch. 11 - Prob. 20PS

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The volume of the sphere x 2 + y 2 + z 2 = r 2 using the disk method.

Solution Summary: The author calculates the volume of a solid region when it is revolved about the x-axis using the disk method.

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To calculate: The volume of the sphere x2+y2+z2=r2 using the disk method.

To calculate: The volume of the ellipsoid x2a2+y2b2+z2c2=1.

Chapter 11 Solutions