SSC CHSL 2024 PYQ — Question 60

The correct answer is option 2 i.e. 64.

Short Trick:

The total number of small spherical balls = R³/r³ = $\frac{8^3}{2^3}$ = 64

Alternate method:

The volume of a sphere = (4/3)πr³, where r is the radius.

The radius of the large sphere (R) = 8 cm

Volume of the large sphere = (4/3)π(8³) = (4/3)π(512) = (2048/3)π cm³

The diameter of each small sphere = 4 cm

So, the radius of each small sphere (r) = 2 cm

Volume of each small sphere = (4/3)π(2³) = (4/3)π(8) = (32/3)π cm³

Number of small spheres = $\frac{(2048/3)\pi}{(32/3)\pi}$ = 64

Therefore, 64 small spherical balls can be obtained.