Question

How many silver coins(cylindrical), 1.75 cm in diameter and of thickness 2 mm, can be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

Answer 1

Let number of silver coins be n

Volume of cuboid = length × breadth × height = 5.5 × 10 × 3.5 = 192.5 $c{m}^3$

Silver coin is a cylinder. Thickness of silver coin is height of cylinder.
Height of coin (cylinder) = h = 2 mm = 0.2 cm

Diameter of coin (cylinder) = d = 1.75 cm

Radius of silver coin (cylinder) = $r=\frac{d}{2}=\frac{1.75}{2}=0.875cm$
Volume of silver coin (cylinder) = $\pi r^{2}h=\frac{22}{7}\times 0.875\times 0.875\times 0.2=0.48125c{m}^3$
According to given condition we have

n × Volume of coin = Volume of cuboid

$\Rightarrow$ n × 0.48125 = 192.5

$\Rightarrow \frac{192.5}{0.48125}=400$