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Question

STATEMENT - 1 : The volume of largest sphere that can be carved out from
cube 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
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B
Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
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C
Statement - 1 is True, Statement - 2 is False
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D
Statement - 1 is False, Statement - 2 is True
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Solution

The correct option is C Statement - 1 is True, Statement - 2 is False
Statement 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 cube
Therefore statement 1 is true but statement 2 is false.

Mathematics

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