Question : The Largest possible sphere is carved out of a cube of side 6 cm. What is the volume of the sphere?
Option 1: $\frac{792}{7}$ cm3
Option 2: $\frac{144}{7}$ cm3
Option 3: $\frac{133}{3}$ cm3
Option 4: $\frac{144}{3}$ cm3
Correct Answer: $\frac{792}{7}$ cm 3
Solution :
Side of cube = diameter of sphere = 6 cm
⇒ Radius, $r$ = 3 cm
$\therefore$ The volume of the sphere
= $\frac{4}{3} \pi r^3$
= $\frac{4}{3}×\frac{22}{7}×3^3$
= $\frac{792}{7}$ cm
3
Hence, the correct answer is $\frac{792}{7}$ cm
3
.
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