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 h
= 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.