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Question

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm?

A
512
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B
500
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C
400
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D
345
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Solution

The correct option is A 512
Volume of the spherical ball of radius 8 cm
=43π×83cm3
Also, volume of each smaller spherical ball of radius 1 cm
=43π×13cm3
Let n be the number of smaller balls that can be made. Then, the volume of the larger ball is equal to the sum of all the volumes of n smaller balls.
Hence, 43π×n=43π×83
n=83=512
Hence, the required number of balls =512.

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