QUESTION

# 2.2 cubic dm of brass is to be drawn into a cylindrical wire of diameter 0.25 cm. Find the approximate length of the wire.

Hint: The volume of the material is given and the diameter of the wire is given. Using the volume of the cylinder formula, $V = \pi {r^2}h$ , we can calculate the length of the wire.

In the given question, a certain volume of brass is to be drawn into a cylindrical wire of diameter 0.25 cm.
The radius of the cylindrical wire is half of the diameter of the cylindrical wire. Hence, we have:
Radius, $r = \dfrac{d}{2}$
$r = \dfrac{{0.25}}{2}$
$r = 0.125cm.........(1)$
Hence, the radius of the cylindrical wire is 0.125 cm.
When the brass is drawn into a cylindrical wire, the volume remains the same.
It is given that the volume of the brass is 2.2 cubic dm.
We know that 1 dm is 10 cm. Hence, we can convert the volume into cubic centimeter as follows:
Volume, $V = 2.2d{m^3} = 2.2 \times {10^3}c{m^3}.........(2)$
We know that formula for the volume of the cylinder. It is given as:
$V = \pi {r^2}h.........(3)$
Using equation (1) and equation (2) in equation (3) and the value of $\pi$ as $\dfrac{{22}}{7}$, we get:
$2200 = \dfrac{{22}}{7}{(0.125)^2}h$
We know that 22 and 2200 cancels and leaves 100 behind in the left-hand side of the equation.
$100 = \dfrac{1}{7}{(0.125)^2}h$
Solving for h, we get:
$h = \dfrac{{100 \times 7}}{{{{\left( {0.125} \right)}^2}}}$
$h = 44800cm$
Expressing the length in meters we get:
$h = 448m$
Hence, the length of the cylindrical wire is 448 m.

Note: Always convert all the values to one particular unit and then substitute in the equation for consistency. Otherwise, the result may differ by the powers of 10, resulting in a wrong answer.