Question

Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm .

Answer 1

Given the diameter of the base of the the circular disc = 1.5 cm
Height = 0.2 cm
Volume of the circular disc = ${\mathrm{\pi r}}^2\mathrm{h}=\mathrm{\pi }\times {\left(\frac{1.5}{2}\right)}^2\times 0.2=\mathrm{\pi }\times {\left(0.75\right)}^2\times 0.2$ ...(i)
Height of the cylinder = 10 cm
Diameter = 4.5 cm
Volume of the cylinder = ${\mathrm{\pi R}}^2\mathrm{H}=\mathrm{\pi }{\left(\frac{4.5}{2}\right)}^2\times 10=\mathrm{\pi }\times {\left(2.25\right)}^2\times 10...\left(\mathrm{ii}\right)$
Now since the circular discs are used to make the cylinder so, let n be the number of circular discs required.
$$\begin{gathered} n\times \mathrm{Volume}\mathrm{of}\mathrm{circular}\mathrm{disc}=\mathrm{Volume}\mathrm{of}\mathrm{cylinder} \\ \Rightarrow \frac{\mathrm{Volume}\mathrm{of}\mathrm{cylinder}}{\mathrm{Volume}\mathrm{of}\mathrm{circular}\mathrm{disc}}=n \\ \Rightarrow \frac{\mathrm{\pi }\times {\left(2.25\right)}^2\times 10}{\mathrm{\pi }\times {\left(0.75\right)}^2\times 0.2}=n \\ \Rightarrow n=450 \end{gathered}$$
Hence, 450 metallic circular discs need to be melted to form the right circular cylinder.