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

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300

200

400

500

answer is C.

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Detailed Solution

Given that the dimensions of the coin is

1.75 cm

in diameter and of thickness 2mm and a cuboid of dimensions

5.5 cm × 10 cm × 3.5 cm

.
10mm=1cm,
2mm=0.2cm
We have the following formulae,
Volume of the cuboid =

l × b × h

Volume of the cylinder =

π r 2 h

The radius will be,
r = 0.875
Volume of coins

= 227 × (0.875) 2 × 0.2 = 0.48125 cm 3

Volume of cuboid=

5.5 cm × 10 cm × 3.5 cm

=192.5

cm 3

Number of coins will be,

= V cuboid V lcoin = 192.5 0.48125 = 400

Thus, the number of coins will be 400.
Therefore the correct option is 3.

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