Question

What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Answer 1

Answer:

The Ratio of the volumes of a cylinder, a cone and a sphere is 3 : 1 : 2  

Step-by-step explanation:

Given :

Diameter and heights of the cylinder, cone, and sphere are same.

Diameter = 2r

Radius = diameter/2 = 2r/2 = r  

Let the radius of the cylinder = radius of the cone  =  radius of the sphere = r

Height of the cone =  Height of the Cylinder =  diameter of Cylinder = 2r

Volume of cylinder :  Volume of cone : Volume of sphere

πr²h : ⅓ πr²h : 4/3πr³

r²h : ⅓ r²h : 4/3r³

r²(2r) : ⅓ r²(2r) : 4/3× r³

2r³ : 2r³/3 : 4r³/3

1 : 1/3 : 2/3

3 : 1 : 2  

Ratio of the volumes of a cylinder, a cone and a sphere = 3 : 1 : 2  

Hence, the Ratio of the volumes of a cylinder, a cone and a sphere is 3 : 1 : 2  

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

HeRe Is Your Ans ⤵

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Given => cylinder, a cone and a sphere has the same diameter and same height

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Volume Of The Cylinder = Volume Of The cone = Volume Of The sphere

πr²h = (1/3) πr²h = (4/3) πr³

3 : 1 : 2

Hence , 3 : 1 : 2 is the ratio of the volumes of a cylinder, a cone and a sphere

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