Question

The radius of a sphere made up of 64 small spheres of radius 'r' is .

• A. r
• B. 2r
• C. 3r
• D. 4r

Answer 1

The correct option is D 4r

Let the radius of the large sphere be 'R'.

$\text{Volume of large sphere =}\frac{4}{3}𝛑R^3$

$\text{Volume of 64 small spheres =}64\times \frac{4}{3}𝛑r^3$

$\because$ Volume of 64 small spheres = Volume of the large sphere
$\therefore 64\times \frac{4}{3}𝛑r^3$ = $\frac{4}{3}𝛑R^3$

$\Rightarrow 64\times r^3=R^3$

$\Rightarrow 4r=R$

∴ The radius of the sphere made up of 64 small spheres of radius 'r' is 4r.