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Question

The largest sphere is carved out of a cube of a side $$7cm$$. Find the volume of the sphere. 


Solution

The diameter of the largest sphere which can be carved out of a cube of side $$7cm$$ is $$7cm$$.

Radius of the sphere $$=r=\cfrac { 7 }{ 2 } cm$$

Hence volume of the sphere $$=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }$$

Volume of the sphere $$=\cfrac { 4 }{ 3 } \times \cfrac { 22 }{ 7 } \times { \left( \cfrac { 7 }{ 2 }  \right)  }^{ 3 }{ cm }^{ 3 }$$

                                     $$=\cfrac { 4 }{ 3 } \times \cfrac { 22 }{ 7 } \times \cfrac { 343 }{ 8 } =179.66{ cm }^{ 3 }\quad $$

Mathematics

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