How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?


Answer :


The shape of the coin will be like the shape of a cylinder of radius
\( \frac{1.75}{2} \ = \ 0.875 \) cm and of height 2 mm = 0.2 cm

Its volume \(= \ \pi r^2 h \ \)

\( = \ \frac{22}{7} \ × \ 0.875 \ × \ 0.875 \ × \ 0.2 \)

\(= \ 0.48125 \) cm3

Volume of the cuboid \(= \ 5.5 \ × \ 10 \ × \ 3.5 \ = \ 192.5 \) cm3

Number of coins required to form the cuboid

\( = \ \frac{Volume \ of \ the \ cuboid}{Volume \ of \ the \ coin} \ \)

\( = \ \frac{192.5}{0.48125} \ = \ 400 \)

\(\therefore \) 400 coins must be melted to form a cuboid.

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