Question

If a sphere of radius $9cm$ is cut into 27 smaller spheres then, the radius of each smaller sphere is .

• A. $3cm$
• B. $6cm$
• C. $9cm$
• D. $12cm$

Answer 1

The correct option is A $3cm$

Let, the radius of the smaller sphere be $r$.

Given: Radius of initail sphere is $9cm$.

We know that, in the given situation, volume remains constant.

Volume of sphere is $\frac{4}{3}\pi r^3$.

$\text{Initial volume = Final volume}$
$\Rightarrow \frac{4}{3}\pi \left(9^3\right)=27\times \frac{4}{3}\pi r^3$
$\Rightarrow 9^3=27\times r^3$
$\Rightarrow 3cm=r$

Thus, radius of each smaller sphere is 3 cm.