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

Volume of Cylinder = Volume of all Cubes melted

Use the Hollow cylinder formula to find out the volume of tube and Divide it with the volume of cube
The result will be no. of cubes

Answer 2

Answer:

7813 balls.

Step-by-step explanation:

Given:

• Radius of the plastic balls, $\rm r=1\ cm.$
• Thickness of the tube, $\rm t=2\ cm.$
• Length of the tube, $\rm L = 90\ cm.$
• Outer radius of the tube, $R=30\ cm.$

Let the inner radius of the tube be $\rm R_o$, such that, $\rm R_o = R-t=30\ cm -2\ cm=28\ cm.$

The tube is in the shape of a cylindrical shell, therefore the volume of the tube is given by

$\rm V_{tube}=\pi (R^2-R_o^2)L=\pi (30^2-28^2)\times 90=32798\ cm^3.$

The volume of one plastic ball is given by

$\rm V_{ball} = \dfrac 43 \pi r^3=\dfrac 43 \times \pi \times 1^3=4.189\ cm^3$

If there are $\rm n$ number of balls which are melted to form the tube, then,

$\rm n\times V_{ball} = V_{tube}\\n\times  4.189 =32798 \\n=\dfrac{32798}{4.189}\approx7813$