A cone,a hemisphere and a cylinder stand on equal bases and have some height . Show their volumes are in ratio 1:2:3
Answers
Answer:
A cone, a hemisphere, and a cylinder stand on equal bases.
Hence 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 V
C
=
3
1
πr
2
h...….(1)
Volume of hemisphere V
H
=
3
2
πr
2
×r
=
3
2
πr
2
×h
V
H
=
3
2
πr
2
h…….(2)
Volume of cylinder V
c
=πr
2
h...…..(3)
From equation 1,2 and 3
V
C
:V
H
:V
c
=
3
1
πr
2
h:
3
2
πr
2
h:πr
2
h
V
C
:V
H
:V
c
=
3
1
:
3
2
:1
V
C
:V
H
:V
c
=1:2:3
Step-by-step explanation: