Question

A cone and a cylinder have same radius and same height show that their
volumes are in the ratio 1:3.​

Answer 1

Answer
Given.
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





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