A toy is made using a cuboid and a sphere. A hollow cone with outer radius 4 cm, inner radius 3 cm and height 24 cm is formed into a cuboid of length 11 cm and breadth 4 cm. Also, a hollow cylinder of thickness 2 cm, outer radius 5 cm and height 18 cm is formed into a sphere. The sphere is kept above the cuboid and toy is made. Which of the following is true?

Option 2 : Height of cuboid < Height of sphere

∵ The cuboid is made from the hollow cone,

∴ Volume of the cuboid = Volume of the hollow cone

L × B × H = 1/3 × π × (R₁² – R₂²) × h

11 × 4 × H = 1/3 × 22/7 × (16 – 9) × 24

∴ Height of the cuboid = 4 cm

∵ The sphere is made from the hollow cylinder

∴ Volume of the sphere = Volume of the hollow cylinder

Given: Thickness = 2 cm

∴ R₁ – R₂ = 2

⇒ R₂ = 5 – 2 = 3 cm

4/3 × π × R³ = π × (r₁² – r₂²) × h

4/3 × π × R³ = π × (25 – 9) × 18

R³ = 3 × 4 × 18 = 3 × 2 × 2 × 2 × 3 × 3

∴ R = 6 cm

Now, height of the sphere = Diameter = 2 × Radius = 2 × 6 = 12 cm