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Eight identical spheres of radius R are ...

Eight identical spheres of radius R are arranged in contact with each other to form a cubic pattern and is placed inside a cubic container of size just enough to contain them. What fraction of the volume of the container does the spheres occupy

A

0.5233

B

0.2616

C

0.8438

D

0.6808

Text Solution

Verified by Experts

The correct Answer is:
A
Side of cube that just enclose the sphere=4R

Volume of cube`=(4R)^(3)=64R^(3)`, Volume of sphere`=8xx(4)/(3)piR^(3)`, Fraction`=(8xx(4)/(3)pi)/(64)=52.33%`
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