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
B
3πl35
C
πl36
D
2πl37

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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