Sum

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

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#### Solution

Radius of each coin, r = \[\frac{2}{2}\] = 1 cm

Thickness of each coin, h = 2 mm = \[\frac{2}{10}\]= 0.2 cm (1 cm = 10 mm)

Let the number of coins made be n.

It is given that a metal parallelopiped is melted to make the coins.

∴ n × Volume of metal in each coin = Volume of the metal parallelopiped

\[\Rightarrow n = \frac{\text{ Volume of the metal parallelopiped } }{\text{ Volume of metal in each coin } }\]

\[ \Rightarrow n = \frac{16 \times 11 \times 10}{\pi r^2 h}\]

\[ \Rightarrow n = \frac{16 \times 11 \times 10}{\frac{22}{7} \times \left( 1 \right)^2 \times 0 . 2} = 2800\]

\[ \Rightarrow n = \frac{16 \times 11 \times 10}{\pi r^2 h}\]

\[ \Rightarrow n = \frac{16 \times 11 \times 10}{\frac{22}{7} \times \left( 1 \right)^2 \times 0 . 2} = 2800\]

Thus, the number of coins made are 2800.

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