Question

How many solid spheres of radius \(1\) cm can be made from a solid sphere of radius \(8\) cm (assuming no loss of material)?

• A. \(256\)
• B. \(512\)
• C. \(1024\)
• D. \(576\)

Hint:

When reshaping solids without loss, the count scales with the ratio of volumes. For similar shapes, that’s the cube of the linear scale: \(N=(R/r)^3\).

Answer 1

The Correct Option is B

Step 1: Use volume conservation.
Number of small spheres \(= \dfrac{\text{Volume of big sphere}}{\text{Volume of one small sphere}}\).
Step 2: Write volumes using \(V=\dfrac{4}{3}\pi r^3\).
\[ N=\frac{\frac{4}{3}\pi (8)^3}{\frac{4}{3}\pi (1)^3} = \frac{512}{1} = 512. \]
Step 3: Conclude.
Thus, \(512\) small spheres can be made.