Multiple choice

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

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The volume of a sphere is given by the formula (4/3) pi r cubed, making Statement 2's first part true; however, the radius of the largest sphere carved from a cube of side a equals a/2, not a. Because the correct radius is a/2, substituting it into the volume formula gives (4/3) pi (a/2) cubed, which simplifies to (1/6) pi a cubed, proving Statement 1 is true. Therefore, Statement 1 is true and Statement 2 is false.

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