A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, $\frac{1}{4}$ of the water flows out. Then the number of lead shots dropped into the water is

see full answer

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

100

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$n \times$ volume of sphere $= \frac{1}{4}$ volume of cone

$\Rightarrow n \times \frac{4}{3} π r^{3} = \frac{1}{4} . \frac{π R^{2} H}{3}$

$\Rightarrow n \times \frac{4}{3} . \frac{5}{10} . \frac{5}{10} . \frac{5}{10} = \frac{1}{4} . \frac{5.5.8}{3}$

$\Rightarrow n = \frac{1}{4} . \frac{5.5.8}{3} . \frac{3}{4} . \frac{10}{5} . \frac{10}{5} . \frac{10}{5}$

$\Rightarrow n = 100$

Watch 3-min video & get full concept clarity