Question

37. A vessel in the form of an inverted cone. Its height is 8cm and radius of its top is 5cm. The vesel is filled with water. How many spherical lead shots of radius 0.5cm are to be dropped into the vessel, so that one fourth of the water of the vessel flows out.​

Answer 1

Answer:

Radius of cone   =5cm

Height of cone    =8cm

Radius of sphere=0.5cm

Volume of cone is,

1/3 $\pi$ $r^{2}$h = 1/3 $\pi$* 5^2 *8

200/3 $\pi$ $cm^{2}$

volume of lead shot= 4/3 $\pi$ r^3

4/3 $\pi$ * 0.5 ^3

1/6 $\pi$ cm^3

number of lead shots

= 200/3  $\pi$ * 1/4 - 1/6 $\pi$

50$\pi$/3 * 6/$\pi$

= 100