The region in the first quadrant bounded by the graph of
MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region in the first quadrant bounded by the graph of y=4−x2, the x-axis, and the y-axis is revolved about the y-axis. Which statement correctly identifies the appropriate type of cross section for determining the volume of the solid?
(a) Cylindrical shells are required for all slices because the region’s vertical sides are parallel to the axis of revolution.
(b) Washers are needed for every y in 0≤y≤4 since the solid has a hollow center that never touches the axis.
(c) Disks are appropriate for all y in 0≤y≤4 because each cross section meets the axis of revolution.
(d) Washers must be used for 0≤y<4 and disks only at y=4 because the inner radius is zero solely at the very top.