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 up to 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 lead shots dropped in the vessel.

Answer 1

Height (h) of conical vessel = 8 cm

Radius (r₁) of conical vessel = 5 cm

Radius (r₂) of lead shots = 0.5 cm

Let n number of lead shots were dropped in the vessel.

Volume if water in concial vessel = `1/3 piR^2 h`

= `1/3 xx 22/7 xx (5) xx 8`

= `4400/21`cm³

Now, total volume of lead shots = `1/4` of [volume of water in the cone]

= `1/4 xx 4400/21`

= `1100/21` cm³

Since, radius of spherical lead shot (r)

= 0.5 cm = `5/10`cm³

∴ Volume of one lead shot = `4/3 pi r^3`

= `(4/3 xx 22/7 xx 5/10 xx 5/10 xx 5/10)` cm³

∴ Number of lead shots

= `"Total volume of lead shots"/"Volume of one lead shot"`

= `(1100/21)/((4 xx 22 xx 5 xx 5 xx 5)/(3 xx 7xx 1000))`

= 100 

Thus, the required number of lead shorts = 100