Question

Find the length of 11 kg copper wire of diameter 0.4 cm. Given one cubic cm of copper weighs 8.4 gram.
A) 132 m
B) 116 m
C) 111.59 m
D) 104.17 m

Answer 1

Hint: In this we have to find the length of copper wire. We will find the length of copper wire by considering wire as a cylinder. Then by the volume of the cylinder we will find the length.

Complete step by step answer:
The figure of copper wire (cylindrical shape) with diameter is given below:

Given that the diameter of copper wire is 0.4 cm.
Radius of copper wire is 0.2 cm.
Also, given that one cubic cm of wire weights 8.4 grams.
Volume of copper wire of 11 kg = $\dfrac{1}{8.4}\times 11\times 1000$
Volume of copper wire of 11 kg = $\dfrac{110000}{84}c{{m}^{3}}$
Also, the wire has a cylindrical shape.
Volume of copper wire =\[\pi {{r}^{2}}h\]. Where r and h are radius and length of copper wire.
Hence, \[\pi {{r}^{2}}h=\dfrac{110000}{84}\]
\[\pi {{\left( 0.2 \right)}^{2}}h=\dfrac{110000}{84}\].
Let the value of \[\pi \] be $\dfrac{22}{7}$
\[\dfrac{22}{7}\left( 0.04 \right)h=\dfrac{110000}{84}\]
By cross multiplication, we get
\[h=\dfrac{\dfrac{110000}{84}}{\dfrac{22}{7}\left( 0.04 \right)}\]
\[h=\dfrac{\dfrac{5000}{12}}{\left( 0.04 \right)}\]
\[h=\dfrac{416.67}{\left( 0.04 \right)}\]
h = 10416.75 cm.
Since, 1 cm = 0.01 m
By converting cm to m, we get
h = 104.1675 m

Hence the length of 11 kg copper wire is 104.1675 m

Note: In this problem one should know that wire has cylindrical shape. Also know how to convert centimetre to meter i.e. 1 cm = 0.01 m.