Question

A cylindrical tube opened at both the ends is made of the iron sheet which is $2$ cm thick. If the outer diameter is $16$ cm and its length is $100$ cm, find how many cubic centimeters of iron has been used in making the tube?

Answer 1

Given:

Outer diameter of the cylindrical tube, $d=16$ cm

$\Rightarrow$ $r_1=$ outer radius of the cylindrical tube $=8$ cm

$[\because d=16cm]$

$r_2$ = inner radius of the cylindrical tube

=$(r_1$ -thickness of the iron sheet)

$=8-2=6$ cm

Height of the cylindrical tube, $h=100$ cm

Volume of the metal used in making cylindrical tube

= Outer volume of a cylindrical tube $-$ Inner volume

$=\pi r_1^{2}h-\pi r_2^{2}h=\pi h(r_1^2-r_2^2)$

$=\frac{22}{7}\times 100(8^2-6^2)$

$=\frac{22}{7}\times 100(8+6)(8-6)$

$=\frac{22}{7}\times 100\times 14\times 2$

$=2200\times 4=8800c{m}^3$

Hence, $8800c{m}^3$ of iron has been used in making the cylindrical tube.