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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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Best answer

Given: For the cylindrical tube, 

height (h) = 90 cm, 

outer radius (R) = 30 cm,

 thickness = 2 cm 

For the plastic spherical ball, 

radius (r ) = 1 cm 

To find: Number of balls melted.

Inner radius of tube (r) = outer radius – thickness of tube 

= 30 – 2 

= 28 cm 

Volume of plastic required for the tube = Outer volume of tube – Inner volume of hollow tube 

= πR2 h – πr2

= πh(R2 – r2

= π × 90 (302 – 282

= π × 90 (30 + 28) (30 – 28) …[∵ a2 – b2 = (a + b)(a – b)] 

= 90 × 58 × 2π cm3

volume of one plastic ball = 4/3πr13

 = 4/3π x 13

 = 4/3πcm3

(Number of balls to be melted) = ( Volume of plastic required for the tube) / (Volume of one plastic ball)

= (90 x 58 x 2π)/(4/3π)

= (90 x 58 x 2 x 3)/4

= 7830

∴ 7830 plastic balls were melted to make the tube.

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