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, then the number of lead shots dropped in the vessel is​

Answer 1

Answer:

100

Step-by-step explanation:

number of lead shots=volume of water flown out/volume of 1 lead shot

the volume of water flown out=1/4 the volume of the cone

given

the radius of cone=5cm

the height of cone=8cm

volume of cone=1/3πr²h

=1/3*22/7*5*5*8=4400/21cm³

the volume of water flown out=1/4 the volume of the cone

=1/4*4400/21

=1100/21

the volume of 1 lead shot

lead shot is in form of the sphere with

r=0.5 cm

the volume of 1 lead shot=the volume of the sphere

=4/3πr³

=4/3*22/7*0.5*0.5*0.5

=11/21 cm³

number of lead shots=volume of water flown out/volume of 1 lead shot

=1100/21/11/21

=1100/21*21/11

=100

number of lead shots =100