Four solids spheres of the same size are made by melting a solid metallic cylinder of
base diameter 4 cm and height 36 cm. What is the diameter of each sphere?
Answers
Given : 4 solids spheres of the same size are made by melting a solid metallic cylinder of base diameter 4 cm and height 36 cm.
To Find : Diameter of each sphere
Solution:
Diameter of each sphere = 2R cm
Radius of sphere = R cm
Volume of one sphere = (4/3)πR³ cm³
Volume of 4 spheres = 4 x (4/3)πR³ cm³
= (16/3)πR³ cm³
Volume of cylinder = πr²h
r = diameter/2 = 4/2 = 2 cm
h = 36 cm
=> Volume of cylinder = π(2)²*36
= 144 π cm³
Equating Volumes
=> (16/3)πR³ = 144π
=> R³ = 27
=> R = 3
=> 2R = 6
Diameter of each sphere = 6 cm
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Answer:
Diameter of each sphere = 2R cm
Radius of sphere = R cm
Volume of one sphere = (4/3)πR³ cm³
Volume of 4 spheres = 4 x (4/3)πR³ cm³
= (16/3)πR³ cm³
Volume of cylinder = πr²h
r = diameter/2 = 4/2 = 2 cm
h = 36 cm
=> Volume of cylinder = π(2)²*36
= 144 π cm³
Equating Volumes
=> (16/3)πR³ = 144π
=> R³ = 27
=> R = 3
=> 2R = 6
Diameter of each sphere = 6 cm
Step-by-step explanation: