SSC GD 2024 PYQ — Question 51

The correct answer is option 4 i.e. 108.

The volume ( V _hemisphere) of a hemisphere is given by the formula:

V_hemisphere = $\frac{2}{3} \pi r^3$

r = 48 cm

V _hemisphere = $\frac{2}{3} \pi (48)^3 = \frac{2}{3} \pi \times 110592 = 73728 \pi \,$ centimeters 

The volume ( V _sphere) of a sphere is given by the formula:

V _sphere = $\frac{4}{3} \pi r^3$

ball with a radius of 8 cm:

V _sphere  = $\frac{4}{3} \pi (8)^3 = \frac{4}{3} \pi \times 512 = \frac{2048}{3} \pi$ centimeters 

Number of balls  = V _hemisphere / V _sphere = $\frac{73728 \pi}{\frac{2048}{3} \pi}$

Number of balls = $\frac{73728 \times 3}{2048} = \frac{221184}{2048} = 108$

Thus, 108 spherical balls can be made by melting the hemisphere.