Question

The total number of metallic solid spherical balls of radius 2 cm that can be made from a solid metallic sphere of radius 20 cm is

• A. 100
• B. 1000
• C. 10000
• D. 100000

Answer 1

The correct option is B 1000

Let $n$ be the number of solid spherical balls of radius 2 cm.
Thus, the volume of the solid metallic sphere of radius 20 cm is equal to the volume of $n$ solid spherical balls of radius 2 cm.
$\Rightarrow \frac{4}{3}\pi \times (20{)}^3=n\times \frac{4}{3}\pi \times (2{)}^3$
$\Rightarrow 20\times 20\times 20=n\times 2\times 2\times 2$
$\Rightarrow n=\frac{20\times 20\times 20}{2\times 2\times 2}$
$\Rightarrow n=1000$
Hence, the correct answer is option (b).