What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long ?

Answer: Option C

External radius = 6 cm
Internal radius = (6 - 0.25) = 5.75 cm
Volume of material in hollow cylinder :
$$\begin{array}{rl}& =\left[\frac{22}{7}\times \left\{{\left(6\right)}^2-{\left(5.75\right)}^2\right\}\times 15\right]\text{c}{\text{m}}^3\\ & =\left(\frac{22}{7}\times 11.75\times 0.25\times 15\right)\text{c}{\text{m}}^3\\ & =\left(\frac{22}{7}\times \frac{1175}{100}\times \frac{25}{100}\times 15\right)\text{c}{\text{m}}^3\\ & =\left(\frac{11\times 705}{56}\right)\text{c}{\text{m}}^3\end{array}$$
Let the length of solid cylinder be h
Then,
$$\begin{array}{rl}& \frac{22}{7}\times 1\times 1\times h=\left(\frac{11\times 705}{56}\right)\\ & \Rightarrow h=\left(\frac{11\times 705}{56}\times \frac{7}{22}\right)\\ & \Rightarrow h=44.0625\text{cm}\end{array}$$