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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?
Solution
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.
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