Question

Sushant has a vessel, of the form of an inverted cone, open at the top, of height $11cm$ and radius of top as $2.5cm$ and is full of water. Metallic spherical balls each of diameter $0.5cm$ 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 $h=11cm,r_1=2.5cm,r_2=0.25cm$

$25\times$volume of cone$=n\times$Volume of each spherical ball

$25\times \frac{1}{3}\pi r_1^{2}h=n\times \frac{4}{3}\pi r_2^3$

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

${2.5}^2\times 11=n\times 10\left({0.25}^3\right)$

$n=440$