Base radius of circular cone is 20 cm and height 30cm.find the top of the cone another cone whose base is parallel to the given cone and radius 16cm is cut off
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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.
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