Question

A solid iron rectangular block of dimensions 4.4m,2.6cm and 1m is the cost into a hallow cylindrical pipe of internal radius 30cm and thickness 5cm. Find the length of the pipe.​

Answer 1

$\sf{\underline{Solution:}}$

Let the inner radius of the cylindrical pipe be 'r'.

Let the outer radius of the cylindrical pipe be 'R'.


$\sf{\underline{Given:}}$

Inner radius: $\sf{30\:cm}$

Thickness: $\sf{5\:cm}$

Outer radius: $\sf{30\:+\:5\:=\:35\:cm}$


$\sf{\underline{Now:}}$

Length of the cuboid = $\sf{4.4\:m =\:440\:cm}$

Breadth of the cuboid = $\sf{2.6\:m =\:260\:cm}$

Height of the cuboid = $\sf{1\:m =\:100\:cm}$


$\sf{\underline{Formula\:to\:be\:used:}}$

$\boxed{\sf{Vol.\:of\:cuboid= Vol.\:of \: cylindrical\:pipe}}$


$\sf{\underline{Now:}}$

By substituting the above values in this formula, we get:

$\sf{Vol.\:of\:cuboid= Vol.\:of \: cylindrical\:pipe}$

$\sf{(Length \times Breadth \times Height) = [\pi( {r}^{2} - {r}^{2} )h]}$

$\sf{(440 \times 260 \times 100) = [\frac{22}{7} ( {35}^{2} - {30}^{2} )h] }$

$\sf{11440000 =[ \frac{22}{7} (1125 - 900)h] }$

$\sf{11440000 =[ \frac{22}{7} \times 325 \times h] }$

$\sf{h = \frac{(11440000 \times 7)}{(325 \times 22) }}$

$\sf{h = \frac{80080000}{7150}}$

$\sf{h = 11200 \: cm}$

$\boxed{\sf{h = 112 \: m}}$


$\sf{\underline{Therefore:}}$

The length of the pipe is 112 m.

Answer 2

Answer : 112.15 metres

Step by step explanation :

Length of rectangular block : 4.4 m

Breadth of rectangular block :  2.6 m

Height of rectangular block : 1 m

Volume of this rectangular block

= L × B× H

= 4.4 × 2.6 × 1

= 11.44 cu. m

Let the internal radius of the hollow cylindrical pipe be r = 30 cm

Converting into metres = 0.3 m

Thickness = 5 cm = 0.05 m

So,

External radius of the pipe R

= 0.3 + 0.05

= 0.35 m

Now,

As we have to find the length of the pipe, let the length be x metres

Volume of the pipe

= π ( R^2 - r^2 ) × x

= 22/7 × ( 0.35^2 - 0.3^2 ) × x

= 22/7 × (0.1225 - 0.09) × x

= 22/7 × 0.0325x

= 0.72 / 7 × x

= 0.102x cu.m

Now,

Volume of pipe = Volume of rectangular block

0.102x = 11.44

x = 11.44/0.102

x = 112.15 ( approx. )

Therefore,

The length of the pipe is 112.15 m