Question

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 ${\left(\frac{2}{5}\right)}^{th}$ 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?

Answer 1

Given that height $\left(h\right)$ of the conical vessel $=11cm$
Radius $\left(r_1\right)$ of the conical vessel $=2.5cm$
Radius $\left(r_2\right)$ of the metallic spherical balls $=\frac{0.5}{2}=0.25cm$
Assume the number of spherical balls that were dropped in the vessel as 'n'.
Volume of the water spilled out of the vessel = Total volume of the spherical balls dropped

$\frac{2}{5}\times$ Volume of cone $=n\times$ Volume of each spherical ball

$\Rightarrow \frac{2}{5}\times \frac{1}{3}\pi r_1{}^{2}h=n\times \frac{4}{3}\pi r_2^3$

$\Rightarrow r_1^{2}h=n\times 10r_2^3$

$\Rightarrow {2.5}^2\times 11=n\times 10\times {0.25}^3$

$\Rightarrow 68.75=0.15625n$

$\therefore n=440$

$\therefore$ The number of spherical balls that were dropped in the vessel is 440.
Sushant made the arrangement so that the water that flows out, irrigates the flower beds.