A SPHERE , CYLINDER AND A CONE ARE OF THE SAME HEIGHTS AND SAME RADII . FIND THE RATIO OF THEIR VOLUMES ..... FAST ......
A SPHERE , CYLINDER AND A CONE ARE OF THE SAME HEIGHTS AND SAME RADII . FIND THE RATIO OF THEIR VOLUMES ..... FAST ......
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Here's the answer:
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Volume of Sphere = (4/3)Πr²h
Volume of Right circular Cylinder = Πr²h
Volume of Right Circular cone = (1/3)Πr²h
Let heights of cylinder and cone are equal to the diameter of the sphere.
Let radius of sphere = r
& Diameter = 2r
•°• Height of the cylinder = Height of cone = 2r
Also radius of all shapes are equal i. e., 2r
Required Ratio
= sphere : cylinder : cone
(4/3)Πr²h : Πr²h : (1/3)Πr²h
Put h = 2r
= (4×2/3)Πr³ : 2Πr³ : (2/3) Πr³
= (8/3) : 2 : (2/3)
= (4/3): 1 : (1/3)
= 4 : 3 : 1
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Hope it helps