Question

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 1

$required \: number \: of \: coins = \frac{5.5 \times 10 \times 3.5}{2 \times \frac{22}{7} \times \frac{1.75}{2} \times 0.2} \\ \\ \frac{192.5}{ \frac{15.4}{14} } = \frac{192.5}{1.1} = 175$

Answer 2

For a coin : $\sf{r=\frac{175}{200}=\frac{7}{8}cm,h=2mm=\frac{2}{10}cm}$

Let n be the number of coins. Then,

n × Volume of one coin = Volume of a cuboid

= $\sf{n×π{r}^{2}h=l×b×h}$

= $\sf{n \times \frac{22}{7} \times \frac{7}{8} \times \frac{7}{8} \times \frac{2}{10} = 5.5 \times 10 \times 3.5}$

Hence, $\sf{n = \frac{55 \times 10 \times 35 \times 7 \times 8 \times 8 \times 10}{22 \times 7 \times 7 \times 2 \times 10 \times 10} = 400}$