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(B) False.Let $r$ be the radius of the original steel ball and $r_{1}$ be the radius of each new ball formed after melting.The volume of the original

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False

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(B) False.Let $r$ be the radius of the original steel ball and $r_{1}$ be the radius of each new ball formed after melting.The volume of the original ball is $V = \frac{4}{3} \pi r^{3}$.The volume of eight new balls is $8 	imes V_{1} = 8 	imes \left( \frac{4}{3} \pi r_{1}^{3} ight)$.Since the volume remains constant during melting,we have $\frac{4}{3} \pi r^{3} = 8 	imes \frac{4}{3} \pi r_{1}^{3}$.Dividing both sides by $\frac{4}{3} \pi$,we get $r^{3} = 8 r_{1}^{3}$.Taking the cube root on both sides,we get $r = 2 r_{1}$,which implies $r_{1} = \frac{r}{2}$.Therefore,the radius of each new ball is $\frac{1}{2}$ of the original radius,not $\frac{1}{8}$.

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

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Write 'True' or 'False' and justify your answer:$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.