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 two - fifths of the water in the vessel flows out Find how many balls were put in teh vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant ?

Explanation

Height of the conical vessel, h = 11 cm.
Radius of the conical vessel, r = 25 cm.
Volume of the conical vessel
`=1/3pir^(2)h=(1/3pixx2.5xx2.5xx11)cm^(3)`
`=(1/3pixx5/2xx5/2xx11)cm^(3)=((275pi)/12)cm^(3)`.
Volume of water flown out after putting spherical balls
`=(2/5"of"(275pi)/12)cm^(3)=((55pi)/6)cm^(3)`
Radius of each spherical ball,
`R=(0.5)/2cm=0.25cm=(25/100)cm=1/4cm.`
Volume of each spherical ball
`R=0.5/2cm=0.25cm=(25/100)cm=1/4cm.` brgt Volume of each spherical ball
`=4/3piR^(3)=(4/3pixx1/4xx1/4xx1/4)cm"^(3)=(pi/4)cm^(3)`
`:." required number of balls"=("volume of water flown out")/("volume of each spherical ball")=((55pi)/6)xx48/pi=440`.
Value shown : We must not waste water and try to put every drop of it optimum use.