Question

Show that the ratio of the volumes of Cone,Hemisphere and Cylinder of same radii

and same height is 1:2:3.​

Answer 1

Answer:

Your Answer is Below.....

Step-by-step explanation:

Volume of cone = (1/3)πr2h

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2h

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same height

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same heightThat is r = h

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same heightThat is r = hVolume of cone : Volume of hemisphere : Volume of cylinder  = (1/3)πr2h :  (2/3)πr3 : πr2h

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same heightThat is r = hVolume of cone : Volume of hemisphere : Volume of cylinder  = (1/3)πr2h :  (2/3)πr3 : πr2h= (1/3)πr3 :  (2/3)πr3 : πr3

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same heightThat is r = hVolume of cone : Volume of hemisphere : Volume of cylinder  = (1/3)πr2h :  (2/3)πr3 : πr2h= (1/3)πr3 :  (2/3)πr3 : πr3= (1/3) : (2/3) : 1

Volume of cone = (1/3)πr2hVolume of hemisphere = (2/3)πr3 Volume of cylinder = πr2hGiven that cone, hemisphere and cylinder have equal base and same heightThat is r = hVolume of cone : Volume of hemisphere : Volume of cylinder  = (1/3)πr2h :  (2/3)πr3 : πr2h= (1/3)πr3 :  (2/3)πr3 : πr3= (1/3) : (2/3) : 1= 1: 2: 3.

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Answer 2

Given :  Cone,Hemisphere and Cylinder of same radii and same height  

To find : Show that Ratio of volume s of Cone,Hemisphere and Cylinder  is 1:2:3

Solution:

Let say Radius  of cone  , hemisphere & cylinder = r

and height of Cone ,  hemisphere & cylinder = h

now height of Hemisphere = radius of hemisphere  

Hence height of  Cone ,  hemisphere & cylinder  = r

Volume of cone  = (1/3)πr²h  = (1/3)πr³

Volume of hemisphere = (2/3)πr³

Volume of Cylinder = πr²h = πr³

Ration of volume of Cone,Hemisphere and Cylinder

= (1/3) : (2/3) :  1

= 1  : 2  : 3  

QED

Hence verified

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