Architects have designed the following glass structure formed by the intersection of the surfaces z = 0, y = −10, z + x² = 10, and 2x + y = 10. ° 10 5 -10 5 ° 20 2 10 In the role of an energy engineer you have been called on to assess the energy requirements of the building. As such you must compute its volume. Set up a single triple integral that will give the required volume, then compute the integral. The order of integration is dV = dy dz dx.

Rotate the ellipse  x2 a2  +  y2 b2  = 1  around the x-axis to approximate the volume (in units3) of a footbal

Column A 1. Find the volume generated by revolving the first quadrant area bounded by the y² = 8x and its latus rectum (* = 2) about the x-axis. parabola 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus rectum (x = 2) about the latus rectum. 3² 3. Find the volume generated by revolving the area bounded by the parabola about the y-axis. = 8x and its latus rectum (x = 2) 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x-axis about the line y = 6. 5. Find the volume of solid generated by revolving the region bounded by the x-axis and one arc of Y = sin about the x-axis. 6. Find the volume of solid generated by revolving bout the = 4x, x = 0, y = 4 about y = 4. a. 128 5 1408 b. 15 32 d. 3 T cubic units 256 e. 15 T cubic units cubic units π cubic units T cubic units f. 167 cubic units Column B