Question

A sphere a cyliender and a cone have same diameter.the height of the cylinder and also the cone are equal to the diameter of sphere find the ratio of their volume

Answer 1

Let the diameter of sphere, cylinder and cone be 2r

Then their radius will be r

and height of cylinder and cone will be 2r

Hence required ratio = Volume of sphere : Volume of cylinder : Volume of cone

= 4πr3 : 6πr3 : 2πr3

= 2 : 3 : 1

=4/3πr*3:πr*2×2r:1/3πr*2×2r

Answer 2

️Since we know that,

Volume of sphere = 4/3 πr³

Volume of cylinder = πr²h

Volume of cone = 1/3 πr²h

➣ Let the radius of sphere be x

➣ Then diameter of sphere = 2x

Since diameter of sphere = height of cylinder and cone.

➣ So, height of cylinder = that of cone = 2x

✍ If sphere, cylinder and cone have same diameter then they will also have same radius of base.

So, volume of sphere = 4/3 πr³

= 4/3 π(x)³ = 4/3 πx³

Volume of cylinder = πr²h

= πx² × 2x = 2πx³

Volume of cone = 1/3 πr²h

= 2/3 πx³

➣ So, volume of sphere / cylinder / cone

= ( 4/3 πx³ ) : ( 2πx³ ) : ( 2/3 πx³ )

= ( 4/3 ) : ( 2 ) : ( 2/3 )

➣ LCM of their denominators we get,

= ( 4/3 × 3 ) : ( 2 × 3 ) : ( 2/3 × 3 )

= 4 : 6 : 2

✪ Answer⇒ 4 : 6 : 2