Question

How many silver coins 1.75 cm in diameter and of thickness to merta must be melted to form a cuboid of dimensions 5.5 cm into 10 cm into 3.5 cm?

Answer 1

Answer:

Step-by-step explanation:

Dimensions of silver coin

Height= 2 mm = 0.2 cm

Diameter= 1.75 cm

Radius= Diameter/2 = 1.75/2 = 0.875 cm

Dimensions of cuboid

Length= 5.5 cm

Breadth= 10 cm

Height = 3.5 cm

Volume of one silver coin

= pi *(r^2)*h

= 3.141(0.875)(0.875)(0.2)

= 0.481 cm^3

Volume of cuboid

= l * b * h

= 5.5(10)(3.5)

= 192.5 cm^3

No. of coins required to form cuboid

= Volume of cuboid/Volume of one coin

= 192.5/0.481

= 400.207

= 400 (rounded to next nearest number)

The answer is 400

Hope it helps.

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