Question

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

Answer 1

Number of coin were made 2800

Step-by-step explanation:

1. Let number of coin = N

2. Dimension of parallelogram

   Length (L) =16 cm

   Breadth (B) =11 cm

   Height (H)= 10 cm

   Volume of parallelogram $\mathbf{=L\times B\times H=16\times 11\times 10=1760 (cm^{3})}$    ...1)

3. Dimension of coin, which is in cylinder shape

   Diameter of coin (d) = 2 cm

   So

   Radius of coin (r)= 1 cm

   Height of coin(h)= thickness of coin = 2 mm = 0.2 cm

 

  Volume of one coin $\mathbf{=\pi r^{2}h=\frac{22}{7}\times 1^{2}\times 0.2=\frac{4.4}{7} (cm^{3})}$      ...2)

4. Total volume is conserved, means

    Final total volume of N coin= Initial volume of parallelogram

 

    $\mathbf{N\times \frac{4.4}{7}=1760}$

    we can write this

    $\mathbf{N=\frac{1760\times 7}{4.4}}$

    On solving above

   N=2800 = Total number of coin