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Question

The largest sphere is carved out of a cube whose edge is of length $$l$$ units. Find the volume of the sphere.


A
5πl36
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B
3πl35
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C
πl36
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D
2πl37
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Solution

The correct option is C $$\displaystyle \frac{\pi\, l^{3}}{6}$$
The largest sphere carved out will have the diameter equal to the side of the cube. 
Hence, diameter of the sphere $$ = l$$ units
=> Radius of the sphere $$ = \cfrac {l}{2} $$
Volume of a sphere $$ = \cfrac { 4 }{ 3 } \pi { r }^{ 3 } $$
Hence, volume of this sphere $$ = \cfrac { 4 }{ 3 } \times \pi \times { \left( \cfrac { l }{ 2 }  \right)  }^{ 3 } =\cfrac { \pi { l }^{ 3 } }{ 6 } $$


Mathematics

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