Question

A cube of copper of edge 11 cm is melted and formed into a cylindrical wire of diameter 0.5 cm. What length of wire will be obtained from the cube?
A. 67.76 m
B. 76.67 m
C. 60 m
D. 70 m

Answer 1

Hint: It is given that the cube is melted to form a cylindrical wire, so we should compare the volumes as the volumes of the cube and the cylinder would be the same. We will use the formula for the volume of cube as, ${{a}^{3}}$, where a is the edge of the cube and for cylinder, we will use the formula, $\pi {{r}^{2}}h$, where r is the radius of the base, h is the height and $\pi =\dfrac{22}{7}$.

Complete step by step solution:
In this question, a cube of copper of edge 11 cm is melted and formed into a cylindrical wire of diameter 0.5 cm and we have to find the length of the wire.

So, as it is given in the question that the copper cube is melted and transformed into a wire, we can say that the volume remains unchanged. Thus, we can compare the volumes of the cube and the cylindrical wire to find the length of the wire. So, we will find the volume of the cube first. We can find the same by using the formula ${{a}^{3}}$, where a is the edge of the cube. Now, the edge of the cube is given as 11 cm, hence the volume of the cube will be,
${{a}^{3}}={{\left( 11 \right)}^{3}}=1331c{{m}^{3}}$
Now, we know that the volume of both the cube and the cylindrical wire is the same, so we can say that the volume of the cylinder will be $1331c{{m}^{3}}$. We can find the volume of the cylinder by using the formula, $\pi {{r}^{2}}h$, where we have $\pi =\dfrac{22}{7}$ and 0.5 cm as the diameter or 0.25 cm as the radius as diameter is twice the radius. We will consider the height of the wire as h. So, we can write as,
$\pi {{r}^{2}}h=1331$
On substituting the values of $\pi =\dfrac{22}{7}$ and radius, r as 0.25 cm or $\dfrac{1}{4}$ cm, we get,
$\begin{align}
  & \dfrac{22}{7}\times {{\left( \dfrac{1}{4} \right)}^{2}}\times h=1331 \\
 & \Rightarrow h=1331\times \dfrac{7\times 16}{22} \\
 & \Rightarrow h=1331\times \dfrac{112}{22} \\
 & \Rightarrow h=6776 \\
\end{align}$
So, we get the value of h as 6776 cm. We know that 100 cm equals 1 m, so we can say that 6776 cm is equal to 67.76 m.
Therefore, the correct answer is option A.

Note: The students should know the basic formulas of area and volume of the different geometric figures and they should be careful with the conversion of units in such types of questions, otherwise they may end up with incorrect answers.