Sushant has a vessel of the form of an inverted cone, open at the top of height 11 cm and Radius of 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 $\frac{2}{5}$th 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?
Given: Height of the conical vessel$=11\ cm$. radius of the top of the vessel$=2.5\ cm$. diameter of the spherical balls=0.5 cm. water flown out from the vessel$=\frac{2}{5} th$ of the water of the vessel.
To do: To find the number of balls put in the vessel.
Solution:
Height (h) of the conical vessel $= 11\ cm$
Radius$( r_{1})$ of the conical Vessel $=2.5\ cm$
Radius$( r_{2})$ of the metallic spherical balls $=\frac{0.5}{2}= 0.25\ cm$
Let n be the number of spherical balls that were dropped in the the vessel
Volume of the water spoiled$=$Volume of the spherical balls droppedin the vessel
$\frac{2}{5}\times$ Volume of cone$=n\times$ Volume of one sphere ball
$\Rightarrow \frac{2}{5}\times\frac{1}{3}\pi r^{2}_{1}h=n\times\frac{4}{3}\pi r^{3}_{2}$
$\Rightarrow r^{2}_{1}h=n\times10r^{3}_{2}$
$\Rightarrow ( 2.5)^2\times11=n\times10\times( 0.25)^{3}$
$\Rightarrow 68.75=0.15625n$
$\Rightarrow n=\frac{68.75}{0.15625}$
$\Rightarrow n=440$
Thus, 440 spherical balls were droped in the vassel.
Sushant made the arrangement so that the water that Tows out, irrigates the flower beds. This shows the judicious usage of water
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