Math, asked by Sagittarius29, 1 year ago

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of their volumes is:-
a) 1:2
b) 2:1
c) 1:7
d) 1:8



Please explain the answer also.

Answers

Answered by abhi178
151
if we cut cone from midpoint then
use similarly concept .
let r is radius of above part and R is the radius of base of cone .
R/r=h/(h/2)=2/1
R=2r
now
volume of cone =πR^2h
=π(2r)^2h=4πr^2h
volume of small cone =πr^2h/2
now,
volume of below part =4πr^2h-πr^2h/2
=7/2 πr^2h

now ratio = volume of above part/volume of below part
=(πr^2h/2)/(7/2πr^2h)=1/7
hence ratio =1:7
option (c) is correct

Sagittarius29: Brilliant answer!!
Sagittarius29: You are a genius
Sagittarius29: I will sure mark it as brainliest if anyone else will gove the answer
Sagittarius29: *give
shivam75: i have a confusion
shivam75: formula of volume of cone is 1/3 pi r2 h
shivam75: not pi r2h
abhi178: yes shivam you are right , but answer is not effected by this
abhi178: i correct it after some time
abhi178: oaky
Answered by darshankrishnasamy22
7

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

Step-by-step explanation:

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