Question : A hollow sphere has an outer radius of 6 cm and inner radius of 3 cm. What is the volume of this hollow sphere?
Option 1: 252$\pi$ cm3
Option 2: 356$\pi$ cm3
Option 3: 144$\pi$ cm3
Option 4: 175$\pi$ cm3
Correct Answer: 252$\pi$ cm 3
Solution :
Outer radius, $R$ = 6 cm
Inner radius, $r$ = 3 cm
Volume of hollow sphere = $\frac{4}{3}×\pi × R^3 - \frac{4}{3}×\pi × r^3$
= $\frac{4}{3}×\pi × 6^3 - \frac{4}{3}×\pi × 3^3$
= $\frac{4}{3}×\pi × ( 6^3 - 3^3)$
= $\frac{4}{3}×\pi × ( 216 - 27)$
= $\frac{4×189}{3}×\pi$
= 252$\pi$ cm
3
Hence, the correct answer is 252$\pi$ cm
3
.
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