16 hemispheres of radius 2 cm are melted to make a single sphere. Find radius of the sphere.

16 cm

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32 cm

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8 cm

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4 cm

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Solution

The correct option is D 4 cm
Let the radii of sphere and hemisphere be $r_{2}$ and $r_{1}$ respectively.

Volume of one hemisphere
$V = \frac{2}{3} π r_{1}^{3}$
Volume of sixteen hemispheres is $16 V$ .

Volume of new sphere:
$V_{2} = \frac{4}{3} π r_{2}^{3}$

According to the question,
$16 V = V_{2}$
$16 \times \frac{2}{3} π r_{1}^{3} = \frac{4}{3} π r_{2}^{3}$
$r_{2}^{3} = 8 r_{1}^{3}$
$r_{2}^{3} = 2^{3} \times 2^{3} c m^{3}$
[Given that: $r_{1}$ = 2 cm ]
$r_{2} = 4 c m$
$r_{2} = 4 c m$

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