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 ?

Given radius of plastic ball, r = 1cm
Thickness of tube = 2cm
Height of tube, h = 90cm
Outer radius, R = 30cm
Inner radius of tube ,r₁ = outer radius – thickness
= 30-2 = 28cm
Volume of plastic needed for tube = volume of outer tube – volume of inner tube
= R²h -r₁²h
= h(R²-r₁²)
= ×90(30²-28²)
= ×90(900-784)
= ×90×116
= 10440cm³
Volume of a plastic ball = (4/3)r³
= (4/3)×1³
= (4/3)cm³
Number of balls melted to make tube = Volume of plastic needed for tube/ Volume of a plastic ball
= 10440÷(4/3)
= 10440×3/4
= 7830
Hence the number of balls needed to make tube is 7830.