Question

How many balls each of radius 1 cm can be made by melting a bigger ball whose radius is 8 cm?

• A. 456
• B. 512
• C. 868
• D. 984

Answer 1

The correct option is B

512

$Volumeofthebigsolidsphere=n\times volumeofthesmallerspheres$

$\frac{4}{3}\pi r^3=n\times \frac{4}{3}\times \pi \times 1^3$ [Volume of a sphere = $\frac{4}{3}\pi r^3$, where r is the radius]

$\frac{4}{3}\pi r^3\times \frac{3}{4}\frac{1}{\pi }=n$
$r^3=n$

$8^3=n$

512 = n
We can make 512 balls of radius 1 cm out of solid sphere of radius 8 cm.