a vessel is in the form of an inverted cone.its height is 8cm and the radius of its top,which is open,is 5cm.it is filled with water up to brim.When lead shots,each of which is a sphere of radius of 0.5cm are dropped into the vessel,one-fourth of the water flows out.find the number of lea shots dropped in the vessel
Answers
Answer:
100
Step-by-step explanation:
Given:
Inverted Cone Radius = 5cm
Height = 8cm
Lead shot(Sphere) Radius = 0.5cm
Known formula:
Volume of cone = 1/3 * pi * r² * h
Volume of a sphere = 4/3 * pi * r³
Let the number of lead shots be n
Water is filled to the brim. So, if we add any extra volume, the same amount of volume of water gets overflown. (Archimedes Principle)
Here,
Extra volume added = Volume of n lead shots
= n * 4/3 * pi * (0.5)³
Volume of the water overflow = 1/4 volume of cone
= 1/4 * 1/3 * pi * (5)² * 8
Equating these two, we get
n * 4/3 * pi * (0.5)³ = 1/4 * 1/3 * pi * (5)² * 8
Multiplying by 3/4 on both sides, we get
=> n * 4/3 * 3/4 * pi * (0.5)³ = 1/4 * 1/3 * pi * (5)² * 8 * 3/4
=> n * pi * (0.5)³ = 1/2 * pi * (5)²
=> n * (0.5)³ = 1/2 * (5)²
=> n * 0.125 = 0.5 * 25
=> n * 0.125 = 12.5
Dividing by 0.125 on both sides, we get
=> n = 12.5 / 0.125 = 100