Question

(27. The height of a cone is 20 cm. A plane
parallel to it's base cuts the cone. If the
1
volume ofsmaller cone so obtained is
8
of the volume of whole cone then, find
the height of smaller cone.

Answer 1

Answer:

Step-by-step explanation:

Volume of a cone of radius r and height h is =  

3

πr  

2

h

​  

 

⇒  

3

1

​  

πr  

2

h=  

125

1

​  

 

3

1

​  

πR  

2

(20)

⇒r  

2

h=R  

2

 

125

(20)

​  

−(1)

Also BE∣∣CD  (given)

In △ABE & △ACD

∠BAE=∠CAD (common )

∠ABE=∠ACD (corresponding angles)

△ABE∼△ACD by AA criterion

thereby the sides will be in proportion

⇒  

CD

BE

​  

=  

AC

AB

​  

 

⇒  

R

r

​  

=  

20

h

​  

−(3)

Substituting (2) in (1) we get  

(  

R  

2

 

r  

2

 

​  

)h=20

⇒(  

20

h

​  

)  

2

h=  

125

20

​  

 

⇒h  

3

=  

5×5×5

20×20×20

​  

 

⇒h=  

5

20

​  

=4cm

Therefore, the section is made (20−4)cm=16cm above the base of original cone.