Question

Notify Me Bookmark

Find the area of the surface S where S is the part of the sphere x2 + y2 + z2 = 81 that lies to the right of the xz-plane and inside the cylinder x2 + z2 = 4.

Find the area of the surface S where S is the part of the sphere x2 + y2 + z2 = 81 that lies to the right of the xz-plane and inside the cylinder x2 + z2 = 4.

Image text
Find the area of the surface S where S is the part of the sphere x 2 + y 2 + z 2 = 81 that lies to the right of the x z -plane and inside the cylinder x 2 + z 2 = 4 .

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

Consider the following. the volume of the solid that lies within both the cylinder x2 + y2 = 16 and the sphere x2 + y2 + z2 = 81 Using cylindrical coordinates, write an integral that can be evaluated to find the volume V of the given solid. (Choose 0 < A ≤ 2π. Choose 0 < B.) V = ∫0 A ∫0 B ∫ −81 − r2 81 − r2 ( )dz dr dθ A = B = Find the volume.
Solution
0 0

(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 64 given the plane. x = k Find the trace. Identify the trace. circle ellipse hyperbola parabola y = k Find the trace. Identify the trace. circle ellipse hyperbola parabola z = k Find the trace. Identify the trace. circle ellipse hyperbola parabola Describe the surface from one of the graphs in the table. ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets (b) If we change the equation in part (a) to x2 − y2 + z2 = 64, how is the graph affected? The graph is rotated so that its axis is the x-axis. The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axis The graph is shifted one unit in the negative y-direction. The graph is shifted one unit in the positive y-direction. (c) What if we change the equation in part (a) to x2 + y2 + 2y − z2 = 63? The graph is rotated so that its axis is the x-axis. The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axis The graph is shifted one unit in the negative y-direction. The graph is shifted one unit in the positive y-direction.(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 64 given the plane. x = k Find the trace. Identify the trace. circle ellipse hyperbola parabola y = k Find the trace. Identify the trace. circle ellipse hyperbola parabola z = k Find the trace. Identify the trace. circle ellipse hyperbola parabola Describe the surface from one of the graphs in the table. ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets (b) If we change the equation in part (a) to x2 − y2 + z2 = 64, how is the graph affected? The graph is rotated so that its axis is the x-axis. The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axis The graph is shifted one unit in the negative y-direction. The graph is shifted one unit in the positive y-direction. (c) What if we change the equation in part (a) to x2 + y2 + 2y − z2 = 63? The graph is rotated so that its axis is the x-axis. The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axis The graph is shifted one unit in the negative y-direction. The graph is shifted one unit in the positive y-direction.
Solution
0 0

Describe the surface. x2 + z2 = 3 sphere ellipsoid hyperboloid circular cylinder elliptic cylinder hyperbolic cylinder parabolic cylinder elliptic paraboloid Sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (Write an equation for the cross section at y = −3 using x and z.) (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 3 using x and z.)
Solution
3 0