ABC26GN4936 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
$1496 \mathrm{cm}^{3}$ of metal is used to cast a pipe of length 28 cm. If the internal radius of the pipe is 8 cm, the outer radius of the pipe is
(a)7 cm
(b)9 cm
(c)10 cm
(d)12 cm
Answer
Explanation
Let the outer radius of the pipe be $R$ cm. Then, volume of metal used = External volume - Internal volume $=\pi R^{2} h-\pi r^{2} h=\pi h\left(R^{2}-r^{2}\right)$ $$\begin{aligned} & =\frac{22}{7} \times 28 \times\left(R^{2}-8^{2}\right)=88\left(R^{2}-64\right) . \\ \Rightarrow & 88\left(R^{2}-64\right)=1496 \Rightarrow R^{2}-64=17 \Rightarrow R^{2}=81 \\ \Rightarrow & R=9 \mathrm{cm} . \end{aligned}$$
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