Question

The volume of a spherical shell whose internal and external diameters are $8cm$ and $10cm$ respectively (in cubic cm) is:

• A. $\frac{122\pi }{3}$
• B. $\frac{244\pi }{3}$
• C. $212$
• D. $257$

Answer 1

Answer: (B)

$\frac{244\pi }{3}$

Given, internal diameter $=8cm$ and external diameter $=10cm$
Volume of a hollow sphere of outer Radius R and inner radius r $=\frac{4}{3}\pi (R^2-r^3)$
Inner radius of the spherical shell $=\frac{8}{2}=4cm$
Outer radius of the spherical shell $=\frac{10}{2}=5cm$
Hence, volume of spherical shell $=\frac{4}{3}\times \pi \times (5^3-4^3)=\frac{4}{3}\times \pi \times 61=\frac{244\pi }{3}{cm}^3$