SSC CPO 2024 PYQ — Question 118

The correct answer is option 4 i.e. 15.68 cm.

Given that

External and internal diameters of the hollow sphere = 10 and 6 cm respectively 

Hence, external and internal radius = 5 and 3 cm respectively 

Radius and height of cone = 5 cm and h respectively 

According to the question 

The volume of the hollow sphere = volume of the cone

Volume of hollow sphere = $\frac{4}{3}$π(R³ - r³)

Volume of cone = $\frac{1}{3}$πr²h

Hence, $\frac{4}{3}$π(5³ - 3³) = $\frac{1}{3}$π(5)²h

Solving for h we get

h = 15.68 cm

Hence, the height of the cone is 15.68 cm.