Question

The internal and external radii of a spherical shell are 8cm and 9cm respectively. Calculate the volume of the material of the shell in cubic cm

Answer 1

Step-by-step explanation:

Let the external and internal radii of spherical shell be R and r cm respectively.

Volume of material of shell = External volume - internal volume

$=\frac{4}{3} \pi R^3 - \frac{4}{3} \pi r^3 \\</p><p>=\frac{4}{3} \pi (R^3 - r^3) \\</p><p>=\frac{4}{3} \pi (9^3 - 8^3)\\</p><p>=\frac{4}{3} \pi (729- 512)\\</p><p>=\frac{4}{3} \times \frac{22}{7}\times 217\\</p><p>=\frac{4}{3} \times 22\times 31\\</p><p>=\frac{4\times 22\times 31}{3}\\</p><p>=\frac{2728}{3}\\</p><p>=909.33\: cm^3$

Hence,

Volume of material of shell =909.33 cubic cm.