Question

Question 1
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 centimetres 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.