Question

find the numberof solid sphereeach radius 0.25cm which may be formed from a solid sphere of radius 4 cm

Answer 1

radius of small sphere (r) = 0.25cm
radius of large sphere (R) = 4 cm
let the total number of small sphere formed = n

$n*volume\ of\ small\ sphere=volume\ of\ large\ sphere\\ \\n* \frac{4}{3} \pi r^3 =\frac{4}{3} \pi R^3 \\ \\n*r^3=R^3\\ \\n= \frac{R^3}{r^3}= (\frac{R}{r})^3 \\ \\n=(\frac{4}{0.25})^3=16^3\\ \\n=\boxed{4096}$

Answer 2

volume of big sphere=4/3*pi*R*R*R
4/3*22/7*64
no.of spheres*volume of 1 small sphere=volume of big sphere
let the no.of sphere be y
y(4/3*22/7*0.25*0.25*0.25)=4/3*22/7*64
4/3 and 22/7 on both sides get cancelled
y=64/0.015625
y=4096
therefore, no.of spheres are 4096