The upper part of the cone has been removed by cutting it by a plane parallel to the base. The curved surface of the remaining part is 8/9 of the total curved surface. At what height?
Answers
Step-by-step explanation:
Assume that the ratio of the altitude of the bigger and the smaller cone be k:1.
Let R and r be the radii of the bigger and the smaller cone respectively.
Let H and h be the height of the bigger and the smaller cone respectively.
Consider the similar triangles △ AGC & △ AFE ,
By the property of similarity, we have,
AF
AG
=
FE
GC
H
h
=
R
r
=
k
1
, where k is some constant.
Curved surface area of bigger cone = πRL, where L is the slant height of the bigger cone.
Curved surface area of smaller cone = πrl, where l is the slant height of the smaller cone.
Again by the property of similarity, we have,
L
l
=
R
r
=
k
1
Given that the ratio of the curved surface area of the frustum of the cone to the whole cone is
9
8
.
The ratio of the curved surface area of the smaller cone to the bigger cone is
9
1
.
πRL
πrl
=
k
2
1
=
9
1
k=3
H
h
=
3
1
Therefore,
H−h
h
=
3−1
1
=
2
1
Hence, the required ratio is 1:2.
Answer:
2/3*height of cone
Step-by-step explanation:
2
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