6. A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane
parallel to its base. Find
the ratio in the volumes of the two parts of the cone.
Answers
Answer:
△OAB∼△OCD (By AA similarity)
∴
OB
OA
=
CD
AB
⇒
h
h/2
=
10
r
⇒r=
2
10
=5cm
Given that cone cut into two parts through the mid point of its height H=
2
h
Volume of frustum of cone =
3
πH
[R
2
+r
2
+Rr]
=
3×2
πh
[10
2
+5
2
+10×5]=
6
175πh
Volume of cone OAB=
3
1
πr
2
2
h
=
3
1
×π×5
2
×
2
h
=
6
25πh
Required ratio =
6
175πh
6
25πh
=
7
1
Step-by-step explanation:
OAB∼△OCD (By AA similarity)
∴
OB
OA
=
CD
AB
⇒
h
h/2
=
10
r
⇒r=
2
10
=5cm
Given that cone cut into two parts through the mid point of its height H=
2
h
Volume of frustum of cone =
3
πH
[R
2
+r
2
+Rr]
=
3×2
πh
[10
2
+5
2
+10×5]=
6
175πh
Volume of cone OAB=
3
1
πr
2
2
h
=
3
1
×π×5
2
×
2
h
=
6
25πh
Required ratio =
6
175πh
6
25πh
=
7
1
solution