Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 32 − x2, y = x2; about x = 4

Required volume is unit.

Step-by-step explanation:

Given equations of curves,

,

substitute second in first we will get,

When and . Thus both curves intersect at the points (4,16),(-4,16). And thus .

Considering width of the representative rectangle as which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

Now,

Length of generating box=Length of from line x=4(axis of revolution)=circumference of the shell=(4-x)

Width of box=

Hence,

which is required volume of generating area.

q: 92 degrees

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step-by-step explanation: