Question

A metal parallelepiped of measures \[16cm\times 11cm\times 10cm\] was melted to make coins. How many coins were made if the thickness and diameter of each coin was \[2mm\] and \[2cm\] respectively?

Answer 1

Hint: In order to find the number of coins made, we must find the radius first from the diameter given of the coin. And then we will be converting the thickness into centimetres as all other dimensions are in centimetres. And then we must divide the volume of the parallelepiped by the volume of each coin. The obtained value would be the number of coins made.

Complete step-by-step solution:
Now let us briefly talk about the parallelepiped. A parallelepiped is basically a three-dimensional figure formed by six parallelograms. This figure will have \[12\] edges, \[6\] faces, and \[8\] vertices. It is basically a convex figure. The volume of parallelepiped is the area of the base times the height. By analogy, parallelepiped relates with the parallelogram.
The figure of a parallelepiped is shown below-

Now let us find the number of coins that can be made from the parallelepiped.
The radius of coin is \[\dfrac{diameter}{2}=\dfrac{2}{2}=1cm\]
For our convenience, let us convert the thickness into centimetres. We get the thickness as,
\[\Rightarrow 2mm=\dfrac{2}{10}=0.2cm\].
Now let us consider that number of coins that can be made as \[x\].
We are told that the parallelepiped is melted to make the coins. So we can say that,
\[x\times \text{volume of each coin=volume of the parallelepiped}\]
Volume of each coin would be \[\pi {{r}^{2}}h=\times \dfrac{22}{7}\times {{1}^{2}}\times 0.2\]
Now, we get the number of coins made as,
\[x=\dfrac{\text{volume of the parallelepiped}}{\text{volume of each coin}}=\dfrac{16cm\times 11cm\times 10cm}{\times \dfrac{22}{7}\times {{1}^{2}}\times 0.2}=2800\]
\[\therefore \] The number of coins made from the parallelepiped would be \[2800\].

Note: We must be careful while solving mensuration problems with dimensions given because all of them should be possessing the same units. If solved with different units, we obtain the incorrect answers. We know that coins are in cylindrical shape that’s why we used the formula of volume of a cylinder for volume of a coin.