A cone , a hemisphere and a cylinder stand on equal bases and have the same height then their volumes are in the ratio of (A) 3:1:2 (B) 1:2:3 (C) 2:1:3 (D) 3:2:1
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As their base are same,
Say the radius of the base and height is R,
So, The cone’s volume: hemisphere’s Volume : Volume of cylinder.
> 1/3 x π x r^2 x r : 2/3 x π x r^2 x r : π x r^2 x r
> 1/3 x 22/7 x r^3 : 2/3 x 22/7 x r^3 : 22/7 x r^3
> 1 : 2 : 3(option B)
Say the radius of the base and height is R,
So, The cone’s volume: hemisphere’s Volume : Volume of cylinder.
> 1/3 x π x r^2 x r : 2/3 x π x r^2 x r : π x r^2 x r
> 1/3 x 22/7 x r^3 : 2/3 x 22/7 x r^3 : 22/7 x r^3
> 1 : 2 : 3(option B)
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3
Given:
Three figures = Cone, hemisphere and a cylinder
Height = constant = h
To Find:
The ratio of their volumes
Solution:
The volume of cone = 1/3πr²h
The volume of hemisphere = 2/3πr³
The volume of cylinder = πr²h
Volume of their ratios = 1/3πr²h : 2/3πr³ : πr²h
= 1/3πr² : 2/3πr³ : πr³ ( r = h)
= 1/3 : 2/3 :1
= 1: 2:3
Answer: The ratio of their volumes is 1: 2:3
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