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Question

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


A
8 cm
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B
16 cm
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C
4 cm
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D
32 cm
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Solution

The correct option is C 4 cm
Let the radii of sphere and hemisphere be r2 and r1 respectively.

Volume of one hemisphere
V=23πr31
Volume of sixteen hemispheres is 16V.

Volume of new sphere:
V2=43πr32

According to the question,
16V=V2
16×23πr31=43π r32
r32=8r31
r32=23×23 cm3
[Given that: r1 = 2 cm ]
r2=4 cm
r2=4 cm

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