SSC CGL 2023 PYQ — Question 60

The correct answer is option 4 i.e. 2.5 cm.

A spherical ball of lead, 3 cm in diameter

The diameters of two of these balls are $\frac{3}{2}$cm and 2 cm, respectively.

Let the diameter of the third spherical ball be 2n

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

Radius = Diameter ÷ 2

According to the question

⇒ $4 \over 3$ π × $3 \over 2$)³ = $4 \over 3$π × [($3 \over 4$)³ + 1³ + n³]

⇒ $27 \over 8$ = [$27 \over64$ + 1 + n³]

⇒ n³ = ${7 \times 27} \over 64$ - 1 = $189 - 64 \over 64$

⇒ n³ = $125 \over 64$

⇒ n = $5 \over 4$

Hence, the diameter of the third ball = 2 × ($5 \over 4$) = $5 \over 2$ = 2.5 cm