Question

A spherical metallic shell with 10 cm external diameter weighs 1789 $\frac{1}{3}$ g. Find the thickness of the shell if the density of the metal is $7g/c{m}^3$

Answer 1

Volume of metallic portion of shell $=\frac{mass}{density}=\frac{1789\frac{1}{3}}{3}=\frac{5368}{21}c{m}^3$
$=\frac{4}{3}\times \pi (R^3-x^3)=\frac{4}{3}\times \frac{22}{7}\times (5^3-r^3)$
$\therefore 5^3-r^3=\frac{5368}{88}=61$
or $r^3=125-61=64$.
r =4 cm.
$\therefore$ Thickness =R -r =5-4 =1 cm