Question

A big RED spherical balloon (radius = 6a) is filled up with gas. On this balloon six small GREEN spherical balloons (radius = a) are stuck on the surface in a specific manner. As RED balloon is slowly deflated, a point comes when all these six GREEN balloons touch and green balloons arrange themselves in a 3-D closed packing arrangement. At that stage the radius of the RED balloon would have reduced by approximately:

• A. 14.5 times
• B. 9.7 times
• C. 6.0 times
• D. 2.4 times

Answer 1

The correct option is A 14.5 times

$\frac{r^{+}}{r^{-}}=0.414\text{for octahedral void fitted with our red spherical balloon}$
$\frac{r^{+}}{a}=0.414$
$r^{+}=0.414a$
$\text{Initial}{r}^{+}\text{radius}=6a$
$\text{Final}{r}^{+}\text{radius}=0.414a$
$\frac{\text{Initial r}}{\text{Final r}}=\frac{6a}{0.414a}=14.49\text{or}14.5$