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 $1{cm}^3$ of wood has a mass of $0.6g$

• A. $3.432$kg
• B. $4.432$kg
• C. $5.432$kg
• D. $3.12$kg

Answer 1

The correct option is A $3.432$kg

$\because$ Inner diameter $=24cm$
$\therefore$ Inner radius $\left(r\right)=\frac{24}{2}cm=12cm$
$\because$ Outer diameter $=28cm$
$\therefore$ Outer radius $\left(R\right)=\frac{28}{2}cm=14cm$
Length of the pipe $\left(h\right)=35cm$
Outer volume $\pi R^{2}h=\frac{22}{7}\times {\left(14\right)}^2\times 35$
$=21560{cm}^3$
inner volume $\pi r^{2}h=\frac{22}{7}\times {\left(12\right)}^2\times 35=15480{cm}^3$
$\therefore$ Volume of the wood used $=$ outer volume-Inner volume$=21560{cm}^3-15840{cm}^3=5720{cm}^3$
$\therefore$ Mass of the pipe $=5720\times 0.6g$
$=3432g=3.432kg$
Hence, the mass of the pipe is $3.432$kg