Question

The inner diameter of a cylindrical wooden pipe is $24cm$ and its outer diameter is $28cm$. The length of the pipe is $35cm$. Find the mass of the pipe, if $1c{m}^3$ of wood has a mass of $0.6g$.

Answer 1

To find mass, we have to find volume of pipe.

Volume of pipe $=$ Volume of outer cylinder $-$ Volume of inner cylinder

OUTER CYLINDER

Radius of outer cylinder $=r_1=\frac{\text{Diameter of outer cylinder}}{2}=\frac{28}{2}=14\text{cm}$

Height of outer cylinder $=h=35\text{cm}$

Volume of outer cylinder $=\pi r_1^{2}h$

$=\pi \left(14{)}^2\right(35)$

INNER CYLINDER

Radius of inner cylinder $=\frac{\text{Diameter of inner cylinder}}{2}=r_2=\frac{24}{2}=12\text{cm}$

Height of inner cylinder $=h=35\text{cm}$

Volume of inner cylinder $=\pi r_2^{2}h$

$=\pi \left(12{)}^2\right(35)$

Now,

Volume of pipe $=$ Volume of outer cylinder $-$ Volume of inner

Volume of pipe $=\pi \left(14{)}^2\right(35)-\pi (12{)}^2\left(35\right)$

$=\pi \left(35\right)\left(\right(14{)}^2-\left(12{)}^2\right)$

$=\frac{22}{7}\times \left(35\right)\times (14-12)(14+12)$

$=22\times 5\times 2\times 26$

$=5720{\text{cm}}^3$

Now it is given that,

Mass of $1{\text{cm}}^3$ volume $=0.6\text{g}$

$\therefore$ Mass of $5720{\text{cm}}^{3}volume=(5720\times 0.6)\text{g}$

$=\left(\frac{5720\times 0.6}{1000}\right)\text{kg}$

$=3.432\text{kg}$

Therefore, mass of pipe is $3.432\text{kg}$