Question

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm × 10 cm × 7 cm?

Answer 1

Given:

For the silver coins (Cylindrical Shape):

Diameter = 1.75 cm

Radius (r) = `1.75/2` cm

= `175/200` cm

= `7/8` cm

Thickness/height (h) = 2 mm

= `2/10` cm

= `1/5` cm

For the Cuboid:

Length (L) = 11 cm

Breadth (B) = 10 cm

Height (H) = 7 cm

Let the total number of coins required to be melted be n.

n × Volume of one cylindrical coin = Volume of the cuboid

n × πr²h = L × B × H

Taking π = `22/7`:

`n xx (22/7 xx 7/8 xx 7/8 xx 1/5) = 11 xx 10 xx 7`

`n xx ((22 xx 7)/(8 xx 8 xx 5)) = 770`

`n xx (154/320) = 770`

n = `(770 xx 320)/154`

n = 5 × 320

n = 1600

Exactly 1600 silver coins must be melted to form the cuboid.