How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form cuboid of dimensions $5.5 cm \times 10 cm \times 3.5 cm$ .

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400

500

300

200

answer is A.

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Detailed Solution

Given, diameter of coin d= 1.75 cm= 17.5 mm (1 cm = 10 mm)
So, radius of coin r=

\frac{1.75}{2} = 0.875

Thickness of coin t= 2 mm= 0.2 cm (1 cm = 10 mm)
Dimensions of cuboid =

5.5 cm \times 10 cm \times 3.5 cm

Suppose total coins = x
Thus,

x

× 5(coin volume) = volume of box

x \times (π r^{2} h) = length \times breadth \times height

\begin{matrix} x \times \frac{22}{7} \times 0.875 \times 0.875 \times 0.2 = 5.5 \times 10 \times 3.5 \\ x = \frac{5.5 \times 3.5 \times 10 \times 7}{22 \times 0.875 \times 0.875 \times 0.2} \end{matrix}

x = 400 coins

Correct option is 1.

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