Multiple choice

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

  1. $512$
  2. $500$
  3. $400$
  4. $345$
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A Correct answer
Explanation

Volume of large sphere = (4/3)*pi*8^3. Volume of small ball = (4/3)*pi*1^3. Number of balls = 8^3 / 1^3 = 512.

AI explanation

The volume of the solid sphere of lead is found using the formula (4/3)*pi*r^3, yielding (4/3)*pi*8^3. The volume of one smaller ball of radius 1 cm is (4/3)*pi*1^3. Dividing the large sphere's volume by the small ball's volume gives (4/3)*pi*512 divided by (4/3)*pi, which equals 512 balls.

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