Question

A cylinder and a hemisphere have equal bases and equal volumes, then find the ratio of
their heights.

Answer 1

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