If 27 identical small spheres are made out of a big sphere of diameter 6 cm, what is the radius (in cm) of the small sphere?

Correct option is A

Given:

Diameter of bigger sphere =6cm

Number of smaller sphere = 27

Formula Used:

Volume of sphere =$$\frac{4}{3}\times\pi \times (r^3)$$​​

Solution:

Radius of sphere = $$\frac{6}{2} =3cm$$​​

When sphere is melted and carved into smaller balls the volume remains same.

Hence

Volume of bigger sphere = n $$\times$$​ Volume of smaller ball

​$$\frac{4}{3}\times\pi \times (3)^3 = 27\times \frac{4}{3}\times\pi \times (r^3)$$​​

​$$r^3= \frac{27}{27} =1$$​​

​$$r= \sqrt[3]{1} =1cm$$​​