Question

The outer and inner radii of a hollow sphere are 2 cm and 1 cm respectively. Then the volume of the sphere is _____ cm$^3$.

• A. $\frac{88}{3}$
• B. $\frac{77}{3}$
• C. $\frac{66}{3}$
• D. $\frac{55}{3}$

Hint:

For hollow spheres, subtract inner volume from outer volume.

Answer 1

The Correct Option is A

Concept: Volume of hollow sphere: \[ V = \frac{4}{3}\pi (R^3 - r^3) \]
Step 1: Substitute values.
\[ R = 2,\quad r = 1 \] \[ V = \frac{4}{3}\pi (2^3 - 1^3) = \frac{4}{3}\pi (8 - 1) = \frac{4}{3}\pi \cdot 7 \]
Step 2: Simplify.
\[ V = \frac{28}{3}\pi \] Using $\pi = \frac{22}{7}$: \[ V = \frac{28}{3} \times \frac{22}{7} = \frac{88}{3} \]
Hence, the volume is $\frac{88{3}$ cm$^3$.