ABC26GN4934 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
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
Answer
Explanation
External radius $=6 \mathrm{cm}$, Internal radius $=(6-0.25) \mathrm{cm}$ $$=5.75 \mathrm{cm} .$$ Volume of material in hollow cylinder $$\begin{aligned} & =\left\{\frac{22}{7} \times\left[(6)^{2}-(5.75)^{2}\right] \times 15\right\} \mathrm{cm}^{3} \\ & =\left(\frac{22}{7} \times 11.75 \times 0.25 \times 15\right) \mathrm{cm}^{3} \end{aligned} =\left(\frac{22}{7} \times \frac{1175}{100} \times \frac{25}{100} \times 15\right) \mathrm{cm}^{3}=\left(\frac{11 \times 705}{56}\right) \mathrm{cm}^{3} .$$ Let the length of solid cylinder be $h$. Then, $$\begin{aligned} \frac{22}{7} \times 1 \times 1 \times h=\left(\frac{11 \times 705}{56}\right) \Leftrightarrow h & =\left(\frac{11 \times 705}{56} \times \frac{7}{22}\right) \mathrm{cm} \\ & =44.0625 \mathrm{cm} . \end{aligned}$$
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