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8. Find the volume between the cone z = Vx² + y² and the plane z = 10+ x above the disk x2 + y² < 1.

8. Find the volume between the cone z = Vx² + y² and the plane z = 10+ x above the disk x2 + y² < 1.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 5E: For the right circular cylinder, suppose that r=5 in. and h=6 in. Find the exact and approximate a...
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8,9 and 10 please
5. Let W be a cone topped by a sphere of radius 1 centered at the origin with angle 90° at the vertex. Write limits of integration for fw dV in the following coordinates: (a) Cartesian (b) Cylindrical (c) Spherical 6. Write a triple integral for the volume of the region between z = 5 and z = 2 < x2 + y² < 3 and 0 < 0 < n. 10, with 7. Write a triple integral for the volume of the cap of the solid sphere x? +y² +z² < 10 cut off by the plane z = 1. 8. Find the volume between the cone z = Vx² + y² and the plane z = 10 + x above the disk x2 + y² < 1. 9. Let W1 be the unit ball: x2 + y² + z² < 1. Without performing the integration, decide whether each integral is positive, negative, or zero. Give reasons for your decision. (a) .. (b) Wi sin ø dV sø dV CoS 10. Let W2 be the top half of the unit ball: 0 < z< V1 – x² – y². Without performing the integration, decide whether each integral is positive, negative, or zero. Give reasons for your decision. (a) (22 – 2) dV (b) / (-xz) dV W2
Transcribed Image Text:5. Let W be a cone topped by a sphere of radius 1 centered at the origin with angle 90° at the vertex. Write limits of integration for fw dV in the following coordinates: (a) Cartesian (b) Cylindrical (c) Spherical 6. Write a triple integral for the volume of the region between z = 5 and z = 2 < x2 + y² < 3 and 0 < 0 < n. 10, with 7. Write a triple integral for the volume of the cap of the solid sphere x? +y² +z² < 10 cut off by the plane z = 1. 8. Find the volume between the cone z = Vx² + y² and the plane z = 10 + x above the disk x2 + y² < 1. 9. Let W1 be the unit ball: x2 + y² + z² < 1. Without performing the integration, decide whether each integral is positive, negative, or zero. Give reasons for your decision. (a) .. (b) Wi sin ø dV sø dV CoS 10. Let W2 be the top half of the unit ball: 0 < z< V1 – x² – y². Without performing the integration, decide whether each integral is positive, negative, or zero. Give reasons for your decision. (a) (22 – 2) dV (b) / (-xz) dV W2
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