The number of lead balls, each of radius 1 cm that can be made from a sphere of radius 8 cm is ____.

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Detailed Solution

The number of lead balls, each of radius 1 cm that can be made from a sphere of radius 8 cm is 512.
We are given that the radius of one lead ball is 1 cm and radius of the sphere is 8 cm.
We know that the volume of the sphere is

43 π r 3,

where r is the radius of the sphere.
We can calculate the number of lead balls as,

N = Volume of the sphere Volume of 1 lead ball ⇒ N = 43 × 227 × 83 43 × 227 × 13 ⇒ N = 43 × 227 × 512 43 × 227 × 1 ⇒ N = 512

Therefore the number of lead balls that can be made is 512.

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