According to the question,

Diameter of the hemisphere $=2m$

So, the radius of the hemisphere (r) $=1m$

Height of the cylinder $\left( {{h}_{1}} \right)=2m$

Then, the volume of the Cylinder $=\pi {{r}^{2}}{{h}_{1}}={{V}_{1}}$

${{V}_{1}}=\pi {{\left( 1 \right)}^{2}}2$

${{V}_{1}}=22/7\times 2=44/7{{m}^{3}}$

As at each of the ends of the cylinder, hemispheres are attached.

Thus, totally there are $2$ hemispheres.

So, the volume of two hemispheres $=2\times 2/3\times 22/7={{r}^{3}}={{V}_{2}}$

${{V}_{2}}=2\times 2/3\times 22/7\times {{1}^{3}}$

${{V}_{2}}=22/7\times 4/3=88/21{{m}^{3}}$

So,

The volume of the boiler (V) $=$ volume of the cylindrical portion $+$ volume of the two hemispheres

$V={{V}_{1}}+{{V}_{2}}$

$V=44/7+88/21$

$V=220/21{{m}^{3}}$

Hence, the volume of the boiler $220/21{{m}^{3}}$