SSC CPO 2024 PYQ — Question 145

The correct answer is option 4 i.e. 1.6 units.

Given that, radius of metal ball = 3 units

Volume of sphere =${4 \over 3} \pi r^3$

Volume of dice = volume of cube = side³

According to the given question,

Volume of metal ball = Volume of 27 dice + Volume of ball

⇒ ${4 \over 3} \pi r_1^3$ = 27(a³)+ ${4 \over 3} \pi r_2^3$

⇒ ${4 \over 3} \pi (r_1^3 - r_2^3)$ = 27a³

⇒ ${4 \over 3} \times {22 \over 7} \times (3^3 - 1^3)$ = 27a³ 

⇒ 27a³ = ${4 \over 3} \times {22 \over 7} \times 26$

⇒ a³ = 4.035

⇒ a = 1.59 ≈ 1.6 units

Hence the side of the dice is 1.6 units.