A cylinder of radius R is filled with water to its brim. A sphere of the same radius is drowned fully into water. If the volume of water left in the cylinder is equal to half of the volume of the sphere, what is the height of the cylinder?
a) R
b) 2R
c) 3R
d) 4R
Answers
Given : a cylinder of radius R is filled with water to its brim . a sphere of the same radius is drowned fully into water .
the water left in the cylinder is equal to half of the volume of the sphere
To Find : what is the height of the cylinder ?
a) R
b) 2R
c) 3R
d) 4R
Solution:
cylinder of radius R is filled with water to its brim
=> Volume of water = Volume of cylinder = πR²h
h = height of cylinder
a sphere of the same radius is drowned fully into water .
Volume of Sphere = (4/3)πR³
Volume of water Displaced = Volume of Sphere = (4/3)πR³
Volume of water Left = πR²h - (4/3)πR³
water left in the cylinder is equal to half of the volume of the sphere
=> πR²h - (4/3)πR³ = ((4/3)πR³)/2
=> πR²h - (4/3)πR³ =(2/3)πR³
=> πR²h = (6/3)πR³
=> πR²h = 2πR³
=> πR²h = 2πR²R
=> h = 2R
height of the cylinder = 2R
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