Answer:
thickness = 0.29 cm
Explanation:
In order to make fake iron ball [made of gold] we should get mass of fake ball
should be equal to that of Iron ball.So for that we should calculate
volume of iron ball using diameter given ;formula is 4/3 pi r^3
given d= 6 cm;so radius r= 6/2 = 3 cm
then volume of Iron ball = 4/3 *3.14* 3^3 = 113.04 cm^3
So mass of iron ball = volume x density = 113.04 * 5.15 g/cm^3 = 582.156 g
This must be the mass of gold ball ;now calculate volume of gold ball using its
density
volume of gold ball = mass of gold ball/density of gold ball = 582.156 g/19.3 g/cm^3
= 30.1635 cm^3
Now this must be the volume of hollow sphere whose outer radius R = 3cm
and inner radius r= ??
Volume of hollow ball = 4/3pi[R3-r^3]
30.1635 cm^3 = 4/3 pi [3^3-r^3]
30.1635* 3/4*3.14 = 27 - r^3
7.2046 = 27- r^3
r^3 = 19.7954
r= 2.7051 cm
So the thick ness = outer radius- inner radius = 3 - 2.7051 = 0.2949 cm
rounding to 2 significant figures
we get thickness = 0.29 cm
