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 ?
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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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