Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Answer 1

Answer:

V1 : V2 : V3 = 1: 2: 3

Step-by-step explanation:

SOLUTION :  

Given :  cone, hemisphere and cylinder have equal base and same height, i.e

h = r  

Volume of cone,V1 : Volume of hemisphere ,V2 : Volume of cylinder  ,V3

V1 : V2 : V3 = (1/3)πr²h :  (2/3)πr³ : πr²h

= (1/3)πr² (r) :  (2/3)πr²(r) : πr²(r)

= (1/3)πr³ :  (2/3)πr³ : πr³

= (1/3) : (2/3) : 1

V1 : V2 : V3 = 1: 2: 3

Hence, V1 : V2 : V3 = 1: 2: 3

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Answer 2

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