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How many smaller hemispheres of radius 4 cm can be formed by melting a hemisphere of radius 16 cm?

1. 16
2. 32
3. 48
4. 64

Correct answer: 64

Solution

The number of smaller hemispheres equals the ratio of the volume of the large hemisphere to the volume of one small hemisphere. Since volume is proportional to r^3, the ratio is (16/4)^3 = 4^3 = 64. So 64 smaller hemispheres can be formed.

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