Q3 of 52 Page 160

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?

Volume of 1 plastic ball = VB


Radius of ball, rB = 1 cm




Length of tube, h = 90 cm


Outer radius of tube, rO = 30 cm


Thickness of tube = 2 cm


Inner radius, rI = 30 – 2 = 28 cm


Volume of tube, VT = Volume of Outer cylinder – Volume of inner cylinder



⇒ VT = 90π(302 - 282)


⇒ VT = 90× 116 × π


Let ‘n’ be the number of balls melted.


⇒ VT = n × VB



⇒ n = 7830 balls


∴ 7830 balls were melted to make the tube.


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