ABC26GN4931 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe is
(a)$3068 \mathrm{cm}^{2}$
(b)$3168 \mathrm{cm}^{2}$
(c)$3268 \mathrm{cm}^{2}$
(d)$3368 \mathrm{cm}^{2}$
Answer
Explanation
External radius, $R=\frac{25}{2} \mathrm{cm}$. Internal radius, $r=\left(\frac{25}{2}-1\right) \mathrm{cm}=\frac{23}{2} \mathrm{cm}$. Length, $h=20 \mathrm{cm}$. Whole surface area $=2 \pi R h+2 \pi r h+2 \pi\left(R^{2}-r^{2}\right)=2 \pi$ $$\left[(R+r) h+\left(R^{2}-r^{2}\right)\right] \begin{aligned} & =2 \times \frac{22}{7} \times\left[\left(\frac{25}{2}+\frac{23}{2}\right) \times 20+\left(\frac{25}{2}+\frac{23}{2}\right)\left(\frac{25}{2}-\frac{23}{2}\right)\right] \\ & =\left(2 \times \frac{22}{7} \times 504\right) \mathrm{cm}^{2}=3168 \mathrm{cm}^{2} \end{aligned}$$
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