Question

Find the radius of the sphere made up of 216 small spheres of radius 'r' ?

• A. 2r
• B. 4r
• C. 6r
• D. 8r

Answer 1

The correct option is C 6r

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

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

$\text{Volume of 216 small spheres =}216\times \frac{4}{3}𝛑r^3$

Here,
Volume of 216 small spheres = Volume of the large sphere

$\Rightarrow 216\times \frac{4}{3}𝛑r^3=\frac{4}{3}𝛑R^3$

$\Rightarrow 216r^3=R^3$

$\Rightarrow 6r=R$

∴ The radius of the sphere made up of 216 small spheres of radius 'r' is 6r.