Question

The number of spheres of radius 'r' merged to make a large sphere of radius '3r' are .

• A. 3
• B. 9
• C. 27
• D. 18

Answer 1

The correct option is C 27

Let, the number of spheres merged be 'y'.

$\text{Volume of y spheres =}y\times \frac{4}{3}𝛑r^3$

$\text{Volume of large sphere =}\frac{4}{3}𝛑(3r{)}^3$

Here,
Volume of y spheres = Volume of large sphere

$\Rightarrow y\times \frac{4}{3}𝛑r^3$ = $\frac{4}{3}𝛑(3r{)}^3$

$\Rightarrow y\times r^3=27r^3$

$\Rightarrow y=27$

∴ The number of spheres merged to make a larger sphere of radius 3r are 27.