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

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.

Solution:

We have,

Length of the rectangular block, $l=4.4 \mathrm{~m}$,

Breadth of the rectangular block, $\mathrm{b}=2.6 \mathrm{~m}$,

Height of the rectangular block, $h=1 \mathrm{~m}$,

Internal radius of the cylindrical pipe, $r=30 \mathrm{~cm}=0.3 \mathrm{~m}$ and

Thickness of the pipe $=5 \mathrm{~cm}=0.05 \mathrm{~m}$

Also, the external radius of the pipe $=0.3+0.05=0.35 \mathrm{~m}$

Let the length of the pipe be $H .$

Now,

Volume of the pipe $=$ Volume of the block

$\Rightarrow \pi R^{2} H-\pi r^{2} H=l b h$

$\Rightarrow \pi\left(R^{2}-r^{2}\right) H=l b h$

$\Rightarrow \frac{22}{7} \times\left(0.35^{2}-0.3^{2}\right) H=4.4 \times 2.6 \times 1$

$\Rightarrow \frac{22}{7} \times(0.1225-0.09) H=4.4 \times 2.6$

$\Rightarrow \frac{22}{7} \times 0.0325 \times H=4.4 \times 2.6$

$\Rightarrow H=\frac{4.4 \times 2.6 \times 7}{22 \times 0.0325}$

$\therefore H=112 \mathrm{~m}$

So, the length of the pipe is 112 m.

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