Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of the top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

Height of the conical vessel, h = 11 cm

Radius of conical vessel, r₁ = 2.5 cm

Radius of metallic spherical ball, r₂ = d/2 = 0.5/2 = 0.25 cm

Let n be the number of metallic spherical balls that were dropped in the conical vessel.

We know that volume of cone = πr²h/3

And volume of sphere = 4πr³/3

Volume of water spilled = Volume of spherical balls dropped

⇒ 2(Volume of cone)/5 = n(Volume of one spherical ball)

⇒ πr₁²h = n × πr₂³

⇒ r₁²h = n × 10r₂³

⇒ (2.5)²(11) = n × 10 (0.25)³

⇒ 68.75 = 0.15625 n

⇒ n = 440

Value: Sushant’s love for plants, nature and environment has been depicted. Plants give us oxygen and the greenery is pleasing to the eyes.

Ans. 440 balls were put in the vessel.