Question : What is the volume of the largest sphere that can be carved out of a wooden cube of sides 21 cm?$\left(\pi=\frac{22}{7}\right)$
Option 1: 3851 cm3
Option 2: 6858 cm3
Option 3: 4851 cm3
Option 4: 5821 cm3
Correct Answer: 4851 cm 3
Solution :
The largest sphere that can be carved out of a cube of side 21 cm will have a diameter of 21 cm.
So, the radius of the sphere, $r$ = $\frac{21}{2}$ cm
Now the volume of the sphere
= $\frac{4}{3}\pi r^3$
= $\frac{4}{3}×\frac{22}{7}×\frac{21}{2}×\frac{21}{2}×\frac{21}{2}$
= 4851 cm
3
Hence, the correct answer is 4851 cm
3
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