  Question

STATEMENT - 1 : The volume of largest sphere that can be carved out fromcube of side a cm is $$\displaystyle \frac{1}{6} \pi a^3$$STATEMENT - 2 : Volume of sphere is $$\displaystyle \frac{4}{3} \pi r^3$$ and for largest sphere to carved from cube radius of sphere $$=$$ side of cube

A
Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1  B
Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1  C
Statement - 1 is True, Statement - 2 is False  D
Statement - 1 is False, Statement - 2 is True  Solution

The correct option is C Statement - 1 is True, Statement - 2 is FalseStatement 1:Edge of cube$$=a\ cm$$Radius of sphere$$=\cfrac { a }{ 2 }$$$$\therefore$$Volume of sphere$$=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }=\cfrac { 4 }{ 2 } \times \pi \times \cfrac { a }{ 2 } \times \cfrac { a }{ 2 } \times \cfrac { a }{ 2 }$$$$=\cfrac { 1 }{ 6 } \pi { a }^{ 3 }$$Statement 2: Radius of sphere$$=\cfrac { 1 }{ 2 } \times$$side of cubeTherefore statement 1 is true but statement 2 is false. Mathematics

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