A solid toy is shaped like a right circular cylinder with a hemispherical end and a cone at the other end. The common diameter is 4.2cm, and the cylindrical and conical portions have heights of 12cm and 7cm, respectively. Determine the volume of the solid. $\left(Take\pi =22/7\right)$

Given solid is a combination of cylinder, cone and hemisphere. Because the volume of a hemisphere is half that of a sphere, it is written as 

Volume of hemisphere $\frac{2}{3}\pi r^3$, where r is the radius of the hemisphere.

Volume of the cone is $=\frac{1}{3}\pi r^2{h}_1$

Volume of the cylinder is $= \pi r^2{h}_2$

To find the volume of the solid, add the volumes of all the shapes.

Diameter of base of conical part $=4.2 \mathrm{cm}$

Diameter of base of cylindrical part $=4.2 \mathrm{cm}$

Diameter of hemispherical part $=4.2 \mathrm{m}$

Therefore radius $=2.1 \mathrm{cm}$

Height of conical part, $h_1=7 \mathrm{cm}$

Height of cylindrical part, $h_2=12 \mathrm{cm}$

Volume of toy = volume of cone + volume of cylinder + volume of hemisphere $=\frac{1}{3}\pi r^2{h}_1+\pi r^2{h}_2+\frac{2}{3}\pi r^3$

$=\pi r^2\left(\frac{h_1}{3}+h_2+\frac{2r}{3}\right)$

$=\frac{22}{7}\times 2.1\times 2.1\left(\frac{7}{3}+12+\frac{2\times 2.1}{3}\right)$

$=\frac{22}{7}\times 2.1\times 2.1\times 15.73$

$=218.06{ \mathrm{cm}}^3$