Question

How many coin-shaped solids of 1 cm radius and 0.2 cm thickness can be made by melting a solid metal brick of length 16 cm, width 11 cm and height 10 cm?

Answer 1

Radius of the cylindrical coin-shaped solids = 1 cm
Thickness of the cylindrical coin-shaped solids = 0.2 cm
Volume of a cylinder = πr²h
= π ×1 × 1 × 0.2
= 0.2 π cm³
Height of the solid metal brick = 10 cm
Length of the solid metal brick = 16 cm
Width of the solid metal brick = 11 cm
Volume of a cuboid = l × b × h
= 10 × 16 × 11
= 1760 cm³
Let the number of cylindrical coin-shaped solids required be n.
The volume of the cuboid will be equal to the collective volume of all the cylindrical coin-shaped solids.
∴ 0.2 π × n = 1760
$$\begin{gathered} \Rightarrow 0.2\times \frac{22}{7}\times n=1760 \\ \Rightarrow n=\frac{1760\times 7}{0.2\times 22} \end{gathered}$$
⇒ n = 2800
∴ The number of coin-shaped solids required = 2800