Use the Method of Disks or Washers, or the Method $$y = 4 x ^ { 2 } , y = 8 x - 4 , y = 16 \text {; the } y \text {-axi }$$

question 68

Essay

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
$$y = 4 x ^ { 2 } , y = 8 x - 4 , y = 16 \text {; the } y \text {-axi }$$

---

Definitions:

Stone Weight

A unit of weight commonly used in some countries, equivalent to 14 pounds or about 6.35 kilograms.

Shear

A force that causes parts of a material to slide past one another in opposite directions, relevant in understanding earthquake mechanisms.

Compression

The process of reducing the volume of a material by applying pressure, or in geology, the stress state in which rock is pressed together, increasing its density.

Tension

A force that stretches material or causes it to be pulled apart.