MathematicsA vessel is in the form of an inverted cone. Its height is 16cm and radius of its top, which is open, is 10 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 lead shots dropped.

A vessel is in the form of an inverted cone. Its height is 16cm and radius of its top, which is open, is 10 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 lead shots dropped.

A
800
B
700
C
100
D
50

Solution:

Given,
Height of the cone = 16cm
Radius of the base of the cone = 10cm
Radius of the sphere = 0.5cm
Now,
Volume of cone is given by,

13 π r 2 h ⇒ 13 π × 102 × 16 ⇒ 16003 π c m 3

Volume of lead shot is given by,

43 π r 3

⇒ 43 π × 0.5 3 ⇒ 16 π c m 3

So, the number of lead shots is given by,

Number of lead shots = Volume of cone Volume of sphere ⇒ 16003 π × 14 16 π ⇒ 400 π 3 × 6 π ⇒ 800

Therefore, the number of lead shots dropped are 800.
Hence, the correct option is 1.