A sphere has a radius of 5 m. How many 5cm diameter spheres can it contain?

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To determine how many 5 cm diameter spheres can fit inside a sphere with a radius of 5 m, the volumes of both spheres are calculated using the formula for the volume of a sphere. The large sphere's radius is converted from meters to centimeters, resulting in a volume calculation of 4/3π (500)^3. The volume of a single small sphere is calculated as 4/3π (2.5)^3, leading to an initial estimate of 8,000,000 small spheres. However, this estimate is unrealistic due to the packing efficiency of spheres, which must be considered for an accurate calculation. Understanding the concept of close-packing is essential for resolving this discrepancy.
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Homework Statement


A sphere has a radius of 5 m. How many 5cm diameter spheres can it contain?


Homework Equations


Volume of a sphere= 4/3π r^3


The Attempt at a Solution


5m=500 cm

volume of large sphere/ volume of small sphere
4/3π (500)^3/ 4/3π (2.5)^3

=8,000,000 spheres

This answer doesn't seem reasonable. What am I doing wrong?​
 
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