Question

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm , 90 cm and 30 cm respectively. How many balls were melted to make the tube?

Answer 1

Radius of each plastic ball, R = 1 cm

Outer radius of the tube, r₂ = 30 cm

Thickness of the tube = 2 cm

∴ Inner radius of the tube, r₁ = Outer radius of the tube − Thickness of the tube = 30 − 2 = 28 cm

Length of the tube, h = 90 cm

Let the number of plastic balls melted to make the tube be n.

It given that plastic balls are melted to form the tube.

∴ n × Volume of each plastic ball = Volume of the tube

$$\begin{gathered} \Rightarrow n=\frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{tube}}{\mathrm{Volume}\mathrm{of}\mathrm{each}\mathrm{plastic}\mathrm{ball}} \\ \Rightarrow n=\frac{\mathrm{\pi }\left(r_2^2-r_1^2\right)h}{{\displaystyle \frac{4}{3}}\mathrm{\pi }{R}^3} \\ \Rightarrow n=\frac{\left({30}^2-{28}^2\right)\times 90}{{\displaystyle \frac{4}{3}}\times 1^3} \\ \Rightarrow n=\frac{116\times 3\times 90}{4}=7830 \end{gathered}$$
Thus, the number of plastic balls melted to make the tube are 7830.