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Now note one thing , in next part ...when we find centroid... Hemisphere is symmetry w.r.t X and y axis
.so it's centroid is 0 for X and y co-ordinate...
We only find z co-ordinate of centroid...
3. Use spherical coordinates: a) Evaluate IILr2 + ข้า dV where E is the solid region inside the s...
3. Use spherical coordinates: b) Find the centroid of the solid hemisphere of radius a, centered at the origin and lying above the xy- plane. 3. Use spherical coordinates: b) Find the centroid of the solid hemisphere of radius a, centered at the origin and lying above the xy- plane.
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H
5. Use spherical coordinates to evaluate 1952/x + y? + dv ", over the solid bounded below by the cone z= V8 + y2 and, and above by the sphere z= 11- x2 - y2
Suppose you have to use spherical coordinates to evaluate the triple integral SI z dV where D is the solid region that lies inside the cone z = 22 + y2 and inside the sphere 22 + y2 +22 = 144 D Then the triple ingral in terms of spherical coordinates is given by Select all that apply p3 cos • sin o dp do do D [!] > av = 6*6** ? [!] > av = 6"* )*S" So*%*%**...
8. (12 points) Use spherical coordinates to evaluate SS zdv, where E is the solid that lies above the cone ø= */3 and below the sphere x2 + y2 + z = 42.
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...
Use cylindrical coordinates to evaluate the triple integral ∭E √(x2+y2)dV where E is the solid bounded by the circular paraboloid z = 1-1(x2+y2) and the xy -plane.
Use cylindrical coordinates to evaluate the triple integral J Vi +y2 dV, where E is the solid bounded by the circular paraboloid z 16 -1(z2 +y2) and the xy-plane.
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...