Section 6.4 Quiz 1. If a region in the first quadrant is revolved about the the shell method R x-axis, (a) requires integrating with respect to (b) requires integrating with respect to x. y. (c) cannot be applied. 2. If a region in the first quadrant is revolved about the the shell method R y-axis, (a) requires integrating with respect to (b) requires integrating with respect to x. y. (c) cannot be applied. 3. The region in the first quadrant bounded by = y the solid generated is and = is revolved about the The volume of x y x y-axis. 2π (b) (c) π π 4. The volume of a box with of length 2, 3, and 4 given by the general slicing method is (a) (b) (c) 5. The disk method corresponds to the general slicing method when the cross-sectional areas are given by (a) = ( . A( x) x f x) = . (b) =π ( . A( x) x2 A( x) f x)2 (c) 6. If the region bounded by = cos and the and (0 is revolved around the the y x x- y-axes x x-axis, ≤ ≤ π/2) volume of the solid generated is most easily found using (a) the shell method integrating with respect to x. (b) the shell method integrating with respect to y. (c) the disk method integrating with respect to x. 7. The base of a solid is the unit circle in the and cross-sections through the solid perpendicular to the xy-plane base are equilateral triangles. To find the volume of the solid, you should use (a) the general slicing method. (b) the disk method. (c) the shell method. 8. The region in the first quadrant bounded by = 4 - and the coordinate axes is revolved about the y x2 x-axis. The volume of the solid generated is 2π (b) 2π (c) 2π Quick Quiz 6.4 Answers: 1b 2a 3b 4a 5c 6c 7a 8a
Section 6.4 Quiz 1. If a region R in the first quadrant is revolved about the x-axis, the shell method (a) requires integrating with respect to x. (b) requires integrating with respect to y. (c) cannot be applied. 2. If a region R in the first quadrant is revolved about the y-axis, the shell method (a) requires integrating with respect to x. (b) requires integrating with respect to y. (c) cannot be applied. 3. The region in the first quadrant bounded by y = the solid generated is x and y = x is revolved about the y-axis. The volume of 2π (b) π (c) π 4. The volume of a box with of length 2, 3, and 4 given by the general slicing method is (a) (b) (c) 5. The disk method corresponds to the general slicing method when the cross-sectional areas are given by (a) A( x) = x2 . (b) A( x) = x f ( x) . (c) A( x) =π f ( x)2 . 6. If the region bounded by y = cos x and the x- and y-axes (0 ≤ x ≤ π/2) is revolved around the x-axis, the volume of the solid generated is most easily found using (a) the shell method integrating with respect to x. (b) the shell method integrating with respect to y. (c) the disk method integrating with respect to x. 7. The base of a solid is the unit circle in the xy-plane and cross-sections through the solid perpendicular to the base are equilateral triangles. To find the volume of the solid, you should use (a) the general slicing method. (b) the disk method. (c) the shell method. 8. The region in the first quadrant bounded by y = 4 - x2 and the coordinate axes is revolved about the x-axis. The volume of the solid generated is 2π (b) 2π (c) 2π Quick Quiz 6.4 Answers: 1b 2a 3b 4a 5c 6c 7a 8a
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