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?

Coins are cylindrical in shape as shown in the figure.Given:Height (h1) of cylindrical coins=2 mm=0.2 cmRadius (r) of circular end of coins =1.75/2=0.875 cmLet x coins be melted to form the required cuboid.Volume of cylinder = πr²hVolume of a cuboid =l × b × hWhen a solid is converted from one form to another, the amount of volume remains the sameVolume of x cylindrical coins = Volume of cuboid⇒x × πr²h1=l × b × h⇒x × π × 0.875² × 0.2=5.5 × 10 × 3.5⇒x=5.5 × 10 × 3.5/(π × 0.875² × 0.2)⇒x=192.5/(0.4876)≈400So, the number of coins melted to form such a cuboid is 400.