Question

What is the number of gold coins, each having a radius of 0.875 cm and a thickness of 2 mm, that need to be melted to create a cuboid with dimensions 5.5 cm × 5 cm x 3.5 cm? (Use ∏=22/7 )

• A. 250
• B. 175
• C. 200
• D. 225

Answer 1

Answer:

C. 200

Radius of each gold coin = 0.875 cm
Thickness = 2 mm = 0.2 cm

Each coin is a cylinder.

Volume of one coin:

$= \frac{22}{7} \times (0.875)^2 \times 0.2$

$= \frac{22}{7} \times \left(\frac{7}{8}\right)^2 \times \frac{1}{5}$

$= \frac{22}{7} \times \frac{49}{64} \times \frac{1}{5}$

$= \frac{154}{320} = 0.48125 \text{ cm}^3$

Volume of cuboid:

$V=l\times b\times h$

$= 5.5 \times 5 \times 3.5$
$= 96.25 \text{ cm}^3$

Number of coins:

$\frac{96.25}{0.48125} = 200$

Answer: 200 gold coins