Maths · Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
STATEMENT - 1: The volume of largest sphere that can be carved out from cube of
STATEMENT - 1: The volume of largest sphere that can be carved out from cube of side a cm is \( \frac{1}{6} \pi a^{3} \) STATEMENT - 2: Volume of sphere is \( \frac{4}{3} \pi r^{3} \) 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
Step-by-step solution
For a cube of side a, the largest sphere that can be carved has diameter equal to the side, so radius = a/2. Its volume = (4/3)π(a/2)^3 = (1/6)πa^3, making Statement 1 true. Statement 2 incorrectly claims radius = side of cube, so it is false. Hence, option C is correct.