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1. 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 ?

A. 42.3215 cm

B. 44.0123 cm

C. 44.0625 cm

D. 44.6023 cm

Solution:

External radius = 6 cm
Internal radius = (6 - 0.25) = 5.75 cm
Volume of material in hollow cylinder :

\begin{aligned} = [\frac{22}{7} \times {{(6)}^{2} - {(5.75)}^{2}} \times 15] c m^{3} \\ = (\frac{22}{7} \times 11.75 \times 0.25 \times 15) c m^{3} \\ = (\frac{22}{7} \times \frac{1175}{100} \times \frac{25}{100} \times 15) c m^{3} \\ = (\frac{11 \times 705}{56}) c m^{3} \end{aligned}

Let the length of solid cylinder be h
Then,

\begin{aligned} \frac{22}{7} \times 1 \times 1 \times h = (\frac{11 \times 705}{56}) \\ \Rightarrow h = (\frac{11 \times 705}{56} \times \frac{7}{22}) \\ \Rightarrow h = 44.0625 cm \end{aligned}

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