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Question

If a sphere of radius 9 cm is cut into 27 smaller spheres then, the radius of each smaller sphere is .

A
3 cm
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B
6 cm
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C
9 cm
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D
12 cm
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Solution

The correct option is A 3 cm
Let, the radius of the smaller sphere be r.

Given: Radius of initail sphere is 9 cm.

We know that, in the given situation, volume remains constant.

Volume of sphere is 43πr3.

Initial volume = Final volume
43π(93)=27×43πr3
93=27×r3
3 cm=r

Thus, radius of each smaller sphere is 3 cm.

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