Question

how many solid iron spherical balls each of diameter (1/4)m can be packed in a cuboidal box of size 3m*200cm*100cm

Answer 1

let the radius of the spherical ball r=d/2=(1/4)/2=0.125m
let the number of spherical ball that can be packed in the box =n
volume of the spherical ball V'=n4/3πr³
V'=n4x3.14x(0.125)³/3
V'=n0.0246/3
V'=n8.17x10-³m³
volume of the box,
V=3x2x1 (since 1m=100cm)
V=6m³
This volume must be equal to the volume of the spherical ball
i.e,n8.17x10-³=6
n=6/(8.17x10-³)
n=734 (approx)
I hope this will help you...