Question

a) A cylinder, hemisphere and cone stand on equal base and same height, the Volume ratio is

3:2:1

b) The radius of a solid sphere is 24 cm. 8 spheres can be made from it of 12cm radius

c) radius of the cone is doubled and height is halved, the volume will be halved

d) A river 10m deep and 40m wide is flowing at the rate of 2m per min. 48000m3

water will flow

into the sea from river

e) A cylinder radius is halved and height is doubled, the volume will become halved​

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