%path = "maths/integral/defined/volume/cylinder or rotation" %kind = chindnum["problems"] %level = 12 A company designs a candy in the shape of a little fish. The profile is delimited upward through these functions:
\(y={{ chutil.TX(chiven.f) }}\), 0<=x<{{ chiven.b }}
\(y={{ chutil.TX(chiven.g) }}\), {{ chiven.b }}<=x<{{ chiven.c }}
\(y={{ chutil.TX(chiven.h) }}\), {{ chiven.c }}<=x<{{ chiven.d }}
The downward line is created through mirroring at the x axis.
  1. Sketch the profile.
  2. Calculate the volume of a cylindrical variant of height {{chiven.t}}.
    \(V_p=\) %chq(0)
  3. Calculate the volume created through rotation around the x axis.
    \(V_r=\) %chq(1)