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Complete the following problems. a. Express the area A of the cross-section cut from the ellipsoid x2+16y2+25z2=1 by the plane z=d as a function of d. (The area of an ellipse with semiaxes a and b is ab.) b. Use slices perpendicular to the z-axis to find the volume V of the ellipsoid in part (a). c. Now find the volume of the ellipsoid a2x2+b2y2+c2z2=1. Does your formula give the volume of a sphere of radius a if a=b=c ? a. Express the area A of the cross-section cut from the ellipsoid x2+16y2+25z2=1 by the plane z=d as a function of d. (The area of an ellipse with semiaxes a and is .) A=254(25d2) square units (Type an exact answer, using as needed.) b. Use slices perpendicular to the z-axis to find the volume V1 of the ellipsoid in part (a). V1=380 units cubed (Type an exact answer, using as needed.) c. Now find the volume V2 of the ellipsoid a2x2+b2y2+c2z2=1 V2= units cubed (Type an exact answer, using as needed.) A particle moves in the xyplane in such a way that its position at time t is r(t)=(tsint)i+(1cost)j. a. Graph r(t). The resulting curve is a cycloid. b. Find the maximum and minimum values of v and a. (Hint: Find the extreme values of v2 and a2 first and take square roots later.)