Question

a spherical ball is melted to make eight new identical balls then the radius of each new ball is 1/8th of the radius of the original ball.Is it true ​

Answer 1

Given:-

• A spherical ball is melted to make eight new identical balls.

To find:-

• The radius of each ball is $\dfrac{1}{8}th$ of the radius of the original ball.

Solution:-

Here, Let the radius of sphere be R.

Then, Volume of Spherical ball = $\dfrac{4}{3}\pi R^{3}$      ----- (1)

Since, It is melted and recast into 8 new spherical balls.

∴ Radius of 8 balls be r.

Therefore, Volume of 8 balls = $8\times \dfrac{4}{3}\pi r^{3}$  ---------(2)

Now, From equation (1) and (2) we get,

So, $8\times \dfrac{4}{3}\pi r^{3}$   =  $\dfrac{4}{3}\pi R^{3}$

⇒  r = $\dfrac{1}{2}th \ R$

Therefore, Radius of each balls is $\dfrac{1}{2}th$ of the radius of the original ball.

Hence, It is false.