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5. Use the approach of Cavalieri to prove the formula of Archimedes for the volume of...
(a) Exprss in rectangular, eylindrical, spherical coordinates, the olune of a) the solid enclosed...
Cal 3 question
(a) Exprss in rectangular, eylindrical, spherical coordinates, the olune of a) the solid enclosed by the paraboloid + and the plane z9 b) the solid bounded above and below by the sphere 2 +2+22 -9 and inside by the cylinder+ c) (not spherical) solid inside x2 + y2 + z2-20 but not above-x2 + y2 d) solid within the sphere 2,2 + y2 + z2-9 outside the cone z Vz2 +3/2 and above the ry-plane. e) solid...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2...
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Find the area of the portion of the plane 2x+3y+4z=28 lying above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane. (1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained w...
Find the area of the portion of the plane 2x+3y+4z=28 lying
above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane.
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22 < 36 Area(S)-
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4,...
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4, Rʻ,...). Notation & Terminology: Use V, and S, for the "volume" and "surface area" of an n- dimensional solid sphere. Thus "Volume" is not always in cubic units, it is in units^n. So, similarly “surface area" is in units (n-1) and is the measurement of the boundary. 1. Look up & become familiar with the formulas for V, and S. Start in R', what...
I need assistance with parts (1) and (2) Thank you 3. Use polar coordinates to find...
I need assistance with parts (1) and (2) Thank you
3. Use polar coordinates to find the volume of the solid given in each of the following problems. Choose two of them x2 + y2 and above the disk (1). A solid lies under the cone z = .x2 + y2 = 9 (Answer: 187 ) (2). A solid locates inside the sphere 22 + y2 + 22 = 16 and outside the cylinder x2 + y2 = 4 (Answer:...
Compute the following surface areas: (a) the surface area of that part of the plane z...
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
Question 5. Find the volume of the region D inside the sphere x² + y2 +(2-1)2...
Question 5. Find the volume of the region D inside the sphere x² + y2 +(2-1)2 = 1 and outside the cone making angle /6 with the positive z-axis.
Cal 3 question
(a) Exprss in rectangular, eylindrical, spherical coordinates, the olune of a) the solid enclosed by the paraboloid + and the plane z9 b) the solid bounded above and below by the sphere 2 +2+22 -9 and inside by the cylinder+ c) (not spherical) solid inside x2 + y2 + z2-20 but not above-x2 + y2 d) solid within the sphere 2,2 + y2 + z2-9 outside the cone z Vz2 +3/2 and above the ry-plane. e) solid...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Find the area of the portion of the plane 2x+3y+4z=28 lying
above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane.
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22 < 36 Area(S)-
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4, Rʻ,...). Notation & Terminology: Use V, and S, for the "volume" and "surface area" of an n- dimensional solid sphere. Thus "Volume" is not always in cubic units, it is in units^n. So, similarly “surface area" is in units (n-1) and is the measurement of the boundary. 1. Look up & become familiar with the formulas for V, and S. Start in R', what...
I need assistance with parts (1) and (2) Thank you
3. Use polar coordinates to find the volume of the solid given in each of the following problems. Choose two of them x2 + y2 and above the disk (1). A solid lies under the cone z = .x2 + y2 = 9 (Answer: 187 ) (2). A solid locates inside the sphere 22 + y2 + 22 = 16 and outside the cylinder x2 + y2 = 4 (Answer:...
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
Question 5. Find the volume of the region D inside the sphere x² + y2 +(2-1)2 = 1 and outside the cone making angle /6 with the positive z-axis.
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