Question

A hollow iron pipe is $21cm$ long and its external diameter is $8cm$. If the thickness of the pipe is $1cm$ and iron weighs $8\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$c{m}^3$}\right.$, then the weight of the pipe is :

Answer 1

Step 1: Find the internal radius of the pipe

Height of the pipe(h)$=21cm$

The external radius of the pipe$=\frac{8}{2}=4cm$(Radius is half of the diameter)

The internal radius of the pipe$=4-1=3cm$

Step 2: Find the volume of the pipe

The volume of the iron$=\mathrm{\pi }\left({\mathrm{R}}^2-{\mathrm{r}}^2\right)\mathrm{h}$

$$\begin{gathered} =\frac{22}{7}\times \left(4^2-3^2\right)\times 21 \\ =\frac{22}{7}\times \left(16-9\right)\times 21 \\ =462{\mathrm{cm}}^3 \end{gathered}$$

Step 3: Find the weight of the pipe

Since, the weight of the $1c{m}^3$ of iron is $8g$.

Therefore, the weight of the $462c{m}^3$of iron$=462\times 8=3696g=3.696kg$ [Since, $1000g=1kg$]

Hence, the weight of the pipe is $3.696kg$.