%path = "maths/integral/defined/volume/cylinder or rotation" %kind = kinda["problems"] %level = 12 A company designs a candy in the shape of a little fish. The profile is delimited upward through these functions:
\(y={{ util.tex(g.f) }}\), 0<=x<{{ g.b }}
\(y={{ util.tex(g.g) }}\), {{ g.b }}<=x<{{ g.c }}
\(y={{ util.tex(g.h) }}\), {{ g.c }}<=x<{{ g.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 {{g.t}}.
    \(V_p=\) %include('chcko/getorshow',idx=0)
  3. Calculate the volume created through rotation around the x axis.
    \(V_r=\) %include('chcko/getorshow',idx=1)