NIFT UG 2020 Question Paper with solutions

Question : 27 of 150

Marks: +1, -0

If a hemisphere is melted and four spheres of equal volume are made, then the radius of each sphere will be equal to

Solution:

Let the radius of hemisphere

=R

and radius of each sphere

=r

According to the question,
Volume of hemisphere

=4 ×

Volume of sphere

∴ \;\; \;{2}/{3} π R^{3}=4 × \;{4}/{3} π r^{2}

⇒ \;\; \;{1}/{8} R^{3}=r^{3} ⇒ \;{r^{3}}/{R^{3}}=\;{1}/{8} ⇒ \;{r}/{R}=\;{1}/{2}

∴ \;\; r=\;{R}/{2}=\;{1}/{2}

of the radius of the hemisphere

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