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 water left in the cylinder is equal to half of the volume of the sphere what is the height of the cylinder ?
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 ?
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
Learn More:
If a cylinder of radius 3cm and height 10cm is melted and recast into ...
https://brainly.in/question/12554875
If 3 cubes of 27m^3 each volume is melted to form glass(s) of 44m ...
https://brainly.in/question/22216765