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:

Coins: diameter = 1.75 cm, so radius `r = 1.75/2 = 0.875  cm`; thickness (height) h_coin = 2 mm = 0.2 cm.

Cuboid: 11 cm × 10 cm × 7 cm.

Step-wise calculation:

1. Volume of the cuboid = 11 × 10 × 7

= 770 cm³

2. Volume of one coin = π × r² × h_coin

= π × (0.875)² × 0.2

Exact form: `r = 7/8`, so `r^2 = 49/64` and h_coin = `1/5`. 

Hence, coin volume = `π × 49/320 = (49π)/320 cm^3`.

3. Number of coins required = `"Volume of cuboid"/"Volume of one coin"`
= `770/((49π)/320)` 

= `(770 xx 320)/(49π)`

= `246400/(49π)` ≈ 1600.644...

Since you cannot use a fraction of a coin, you must melt 1601 coins to form the cuboid.