Question

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top which is

open is 5 cm. It is filled with water upto the brim. When lead shots, each of which is a sphere of

radius 0.5 cm are dropped into the vessel, one fourth of the water flows out. Find the number of

shots dropped in the vessel.​

Answer 1

GIVEN:-

$\small\sf\green{height \:(h)\:of\:conical\:vessel=8cm}$

$\small\sf\green{radius \: (r1) \: of \: conical \: vessel=5cm}$

$\small\sf\green{radius\:(r2)\:of\:lead\:shots=0.5cm}$

⠀⠀

$\small\sf\orange{let \: n \: of \: lead \: shots \: were \: dropped \: in \: the \: vessel}$

⠀⠀⠀

$\small\sf\pink{Volume\:of\:water\:spilled=Volume\:of\:dropped\:lead\:shots}$

⠀⠀

$\longrightarrow$$\large\sf\red{\frac{1}{4} \times volume \: of \: cone = n \times \frac{4}{3} {r2}^{2} }$

$\longrightarrow$$\large\sf\red{ \frac{1}{4} \times \frac{1}{3} π {r}^{2} h = n \times \frac{4}{3} π {r2}^{3} }$

$\longrightarrow$$\large\sf\red{{r1}^{2} h = h \times 16 {r2}^{3}}$

$\longrightarrow$$\large\sf\red{{5}^{2} \times 8 = n \times 16 \times {(0.5)}^{3} }$

$\longrightarrow$$\large\sf\red{n = \frac{25 \times 8}{16 \times { ( \frac{1}{2}) }^{3} }}$

$\longrightarrow$$\large\sf\red{n=100}$