Question

A hollow iron pipe 10 cm long has exterior radius equal to 14 cm. If the thickness of the pipe is 4 cm, then the total surface area of the pipe is

• A. $3168c{m}^2$
• B. $2128c{m}^2$
• C. $2112c{m}^2$
• D. $2008c{m}^2$

Answer 1

The correct option is C $2112c{m}^2$

Let $r_1$ and $r_2$ be the internal and external radii of the hollow iron pipe and h be its height, respectively.


$\therefore h=10cm,r_2=14cm$
Also, thickness of pipe is 4 cm.
$\Rightarrow r_2–r_1=4$
$\Rightarrow 14–r_1=4$
$\Rightarrow r_1=10cm$
$\therefore \text{TSA of the pipe}=2\pi (r_1+r_2)h+2\pi (r_2^2-r_1^2)$
$=2\pi (r_1+r_2)[h+(r_2-r_1\left)\right]$
$=2\pi (10+14)[10+(4\left)\right]$
$=2\pi \times 24\times 14$
$=2\times \frac{22}{7}\times 24\times 14$
$=22\times 24\times 4$
$=2112c{m}^2$
Hence, the correct answer is option (c).