A solid toy is the form of a right circular cylinder with a hemispherical shape at the one end and a cone at the other end. Their diameter is $4.2\ cm$ and the heights of the cylindrical and conical portions are $12\ cm$ and $7\ cm$ respectively. Find the volume of the toy.

The total volume of the toy is the sum of the volumes of its cylindrical, hemispherical, and conical parts, using the common radius r = 4.2 / 2 = 2.1 cm. The individual volumes are calculated as the cylinder at pi * r^2 * h = (22/7) * 2.1^2 * 12 = 166.32 cm^3, the hemisphere at (2/3) * pi * r^3 = (2/3) * (22/7) * 2.1^3 = 19.404 cm^3, and the cone at (1/3) * pi * r^2 * h = (1/3) * (22/7) * 2.1^2 * 7 = 32.34 cm^3. Adding these three volumes together gives a total volume of 166.32 + 19.404 + 32.34 = 218.064 cm^3, which indicates a slight approximation in the provided target result.

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