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

The correct option is C: $218c{m}^3$

Given: Diameter of the cylinder, cone, and hemisphere $=4.2cm$

Radius of the cylinder, cone, and hemisphere $=2.1cm$

Height of the cylinder $=12cm$

Volume of the cylinder $=\pi r^{2}h=\pi (2.1{)}^2\times 12c{m}^3$

Height of the cone $=7cm$

Volume of the cone $=\frac{1}{3}\pi r^{2}h=\frac{\pi }{3}\times (2.1{)}^2\times 7c{m}^3$

Volume of hemisphere $=\frac{2}{3}\pi r^3=\frac{2}{3}\times \pi \times (2.1{)}^{3}c{m}^3$

$\therefore$ Volume of the toy $=$ Volume of cylinder $+$ Volume of the Cone + Volume of hemisphere

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

$=\pi (2.1{)}^2\times [12+(\frac{1}{3}\times 7)+(\frac{2}{3}\times 2.1)]$

$=\frac{22}{7}\times 2.1\times 2.1\times \frac{47.2}{3}c{m}^3=218.064c{m}^3$

Hence, the volume of the toy is $218c{m}^3.$