    Question

# What will be the packing fraction in the following case? The sphere is touching the sides of the cube exactly. A

pi/3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

pi/6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

pi/4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

pi/2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B pi/6 We know that, Packing fraction = Volume occupied inside the unit cellVolume of unit cell Here the unit cell is the cube and volume occupied inside the unit cell will be equal to the volume of the sphere. Let's assume the sphere is of radius r and cube is of side a. Volume of sphere will be 43 ∗ pi ∗ r3 Volume of cube will be a3 Notice that the side of the cube is equal to the diameter of the sphere since it is touching all the sides. So, a = d a = 2r Using the relation, we get Packing fraction = 43 ∗ pi ∗ r3(2r)3 = 43 ∗ pi ∗ r38r3 = pi6 = 0.523  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   Packing Fraction and Efficiency
CHEMISTRY
Watch in App  Explore more
Join BYJU'S Learning Program
Select...