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Volume and Surface area of Solids — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsVolume and Surface area of Solids4 Marks
Question
A solid rectangular block of dimensions $4.4\ m, 2.6\ m$ and $1\ m$ is cast into a hollow cylindrical pipe of internal radius $30\ cm$ and thickness ​$5\ cm$. Find the length of the pipe.
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Answer

We have,
Length of the rectangular block, $I=4.4 m$,
Breadth of the rectangular block, $b =2.6 m$,
Height of the rectangular block, $h =1 m$,
Internal radius of the cylindrical pipe, $r =30 cm=0.3 m$ and
Thickness of the pipe $=5 cm=0.05 m$
Also, the external radius of the pipe $=0.3+0.05=0.35 m$
Let the length of the pipe be $H .$
Now,
Volume of the pipe $=$ Volume of the block
$\Rightarrow\pi\text{R}^2\text{H}=\pi\text{r}^2\text{H}=\text{lbh}$
$\Rightarrow\pi(\text{R}^2-\text{r}^2)\text{H}=\text{lbh}$
$\Rightarrow\frac{22}{7}\times(0.35^2-0.3^2)\text{H}=4.4\times2.6\times1$
$\Rightarrow\frac{22}{7}\times(0.1225-0.09)\text{H}=4.4\times2.6$
$\Rightarrow\frac{22}{7}\times0.0325\times\text{H}=4.4\times2.6$
$=\text{H}=\frac{4.4\times2.6\times7}{22\times0.0325}$
$\therefore\text{H}=112\text{m}$
So, the length of the pipe is $112\ m.$

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