We have a raindrop that is obtained by revolving the profile curve:
f(x)=sqrt(x)*(x-C)^2 about the x-axis for 0<=x<=C, with C a positive constant.
a) Sketch the profile curve and solid of revolution.
b) For what value of C will the volume be 1? What are the dimensions, length and diameter, of such a raindrop?
How can I sketch the curve when the C varies, this is a little confusing to me. I don't know how to produce this sketch.
I think to do the volume I just need to set integral of the function pi* (f(x))^2) dx from 0 to C equal to 1 and solve for C. I get (30/pi)^1/6 doing this. I am not sure if this is correct though, and don't know how to find the dimensions. Thanks.