Find the area of the surface generated by revolving the curve about the x-axis. .

Question

Find the area of the surface generated by revolving the curve about the x-axis.  .

Quizplus · Accepted Answer

The curve appears to be a circle centered at (0,-3) with radius 3. To find the area of the surface generated by revolving this circle about the x-axis, we can use the formula:

A = 2π∫(y)(ds)

where y is the y-coordinate of the curve (in this case, y = -3 + 3 = 0), ds is an element of arc length, and the integral is taken over the curve. For a circle of radius r, we have:

ds = r dθ

So, in this case, we have:

A = 2π∫(0)(3 dθ) = 0

This means that there is no surface generated by revolving the curve about the x-axis, since the curve lies in the xz-plane. Therefore, the only answer choice that makes sense is C, which indicates that the area is 0.

Find the Area of the Surface Generated by Revolving the Curve