Question

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?

Answer 1

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

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
= πR²h − πr²h
= πh(R² − r²)
= π × 90 (30² − 28²)
= π × 90 (900 − 784)
= π × 90 × 116 cm³

Volume of one plastic ball = `4/3πr_1^3`
= `4/3π × 1^3`
= `4/3π` cm³

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

= `(cancelπ × 90 × 116)/(4/3 cancelπ)`

= `(90 × 116 × 3)/(4)`

= 90 × 29 × 3

= 7830

Thus, the number of plastic balls melted to make the tube are 7830.