Question

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

Answer 1

Solution:

Radius of coin = 0.875 cm,

height = 0.2 cm

Dimensions of cuboid = 5.5 cm x 10 cm x 3.5 cm

Volume of coin=${πr^2h}$

=π × 0.875 × 0.875 × 0.2

= 0.48125

Volume of cuboid = 5.5 x 10 x 3.5 = 192.5 cm3

Number of coins = 192.5 / 0.48125 = 400

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Answer 2

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400 coins

step-by-step explanation:

Given,

for silver coins,

we know that it is cylinder,

diameter = 1.75 cm

.°. radius, r = 1.75/2 cm

and,

height, h = 2mm = 2/10 cm = 0.2 cm

.°. Volume, V = $π{r}^{2}h$

=> V = $π{(1.75/2)}^{2}×(0.2)$

=> (0.6125π/4) ${cm}^{3}$

Now,

For Cuboid,

length, l = 10 cm

breadth, b = 5.5 cm

height, H = 3.5 cm

.°. Volume, V' = lbH

=> V' = 192.5 ${cm}^{3}$

Now,

Let,

the number of coins be ' n '

now,

it is given that the coins are being melted to form this cuboid

therefore,

the vloume of all coins must be equal to the Volume of the Cuboid

=> nV = V'

=> n = V'/V

=> n = 4×192.5 / 0.6125π

=> n = 4× 314/3.14

=> n = 400

Hence,

400 coins are melted to form the cuboid.