A solid lead sphere of radius 11 cm is melted and recast into small solid spheres of radius 2 cm each. How many maximum number (in integer) of such sphere can be made of ?
Answer & explanation
Correct answer: option 2
We know that,
Volume of a sphere = \(\frac{4}{3}\)πr3
We have,
Radius of solid sphere = 11 cm
Radius of small solid sphere = 2 cm
Volume of the solid sphere with radius 11 cm = \(\frac{4}{3}\)× π × 113
Volume of the small solid sphere with radius 2 cm = \(\frac{4}{3}\)× π × 23
Number of small solid sphere = \(\frac{4}{3}\)× π × 113 $\div$ \(\frac{4}{3}\) × π × 23 = \(\frac{1331}{8}\) = 166