Question

the midpoint of horizontal and is called its​

Answer 1

Answer:

Let the height of the cone be H and base radius be R units.

Then its volume V=

3

1

πR²H cu. units

As the horizontal plane cuts the cone into two parts through the mid point of its axis, the height of the cone is divided into two equal parts, forming a top cone of height

2

H

units. If the base radius of the top cone is r units, then

2

H

r

=

H

R

[Since the vertical angle of both are same].

Solving, r=

2

R

units.

Hence volume of the small cone at the top is:

V=

3

1

π(

2

R

)

2

(

2

H

)=

24

πR

2

H

cu. units

So volume of the bottom part (frustum) is:

V−v=

3

πR

2

H

−

24

πR

2

H

=

24

7

πR

2

H cu. units

Therefore, ratio of their volumes, Top part : Bottom part that is:

24

πR

2

H

:

24

7

πR

2

H=1:7

Hence, the ratio of the volume of the upper part to the volume of lower part is 1:7.