Question

A cone ,a hemisphere and a cylinder stand upon same base and. having equal height . Show that their volumes are in the ratio of 1:2:3​

Answer 1

Answer:

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 height That 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

Step-by-step explanation:

Answer 2

Answer:

 radius of base of cone = radius of hemisphere = radius of cylinder=r

And,

They also have same height =h

Hight of cone =h

Hight of cylinder=h

Hight of Hemisphere r=h   (r is the radius of sphere)

Now,

Volume of cone  VC=1/3πr2h...….(1)

Volume of hemisphere VH=2/3πr2×r

                                              =2/3πr2×h

                                       VH=2/3πr2h……

Volume of cylinder Vc=πr2h...…..(3)

from these equations

ratio = 1:2:3