Question

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

Answer 1

The correct option is C Statement - 1 is True, Statement - 2 is False

Statement 1:

Edge of cube$=acm$

Radius of sphere$=\frac{a}{2}$

$\therefore$Volume of sphere$=\frac{4}{3}\pi r^3=\frac{4}{2}\times \pi \times \frac{a}{2}\times \frac{a}{2}\times \frac{a}{2}$

$=\frac{1}{6}\pi a^3$

Statement 2: Radius of sphere$=\frac{1}{2}\times$side of cube

Therefore statement 1 is true but statement 2 is false.