# Top and bottom are on the sphere defined by the

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top and bottom are on the sphere defined by the equation r 2 + z 2 = 100 and whose lateral boundary is given by the cylinder defined by the equation r = 5 sin( θ ). Do not attempt to evaluate the integral. ( WARNING: r = 5 sin( θ ) has teeth. If you don’t pay attention to the details, it bites.) G 1 dV ______________________________________________________________________ 4. (10 pts.) Write down a triple iterated integral in cartesian coordinates that would be used to find the volume of the solid G bounded by the surface y = x 2 and the planes y + z = 4 and z = 0, but do not attempt to evaluate the triple iterated integral you have obtained. [Sketching the traces in the coordinate planes will help.] G 1 dV

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TEST4/MAC2313 Page 3 of 6 ______________________________________________________________________ 5. (10 pts.) Write down the triple iterated integral in spherical coordinates that would be used to compute the volume of the solid G within the cone defined by φ = π /4 and between the spheres defined by ρ = 4 and ρ = 9 in the first octant . Do not attempt to evaluate the interated integrals. G 1 dV ______________________________________________________________________ 6. (10 pts.) Compute the surface area of the portion of the hemisphere defined by z = (16 - x 2 - y 2 ) 1/2 that lies between the planes defined by z = 1 and z = 2.
TEST4/MAC2313 Page 4 of 6 ______________________________________________________________________ 7. (10 pts.) Compute the work in moving a particle along of the path in

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