Q. A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volume of the two parts.
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Answers
Answer:
ye question acha hai
Step-by-step explanation:
Since the plane divides the cone into two parts through the mid point so, a small cone and a frustum will be formed. Let the radius of the smaller cone be r cm. Hence, the ratio of the volumes of the two parts will be 1 : 7.
The radius of upper cone (R
1
)=
2
4
=2
Bottom radius =4 cm
Volume of upper cone (V
1
)=
3
1
πr
2
h
=
3
1
π×(2)
2
×(
2
h
)
Volume of upper cone(V
1
)=
3
2πh
cm
3
Vol of bottom frustum (V
2
)=
3
πh
(R
1
2
+R
2
2
+R
1
R
2
)
=
3
π(
2
h
)
(4+16+8)
=
3
π(
2
h
)
(28)
Vol of bottom frustum (V
2
)=
6
πh
(28)
V
2
V
1
=
6
πh
(28)
3
2πh
V
2
V
1
=
3
2πh
×
πh×28
6
V
2
V
1
=
7
1
Answer:
Since the plane divides the cone into two parts through the mid point so, a small cone and a frustum will be formed. Let the radius of the smaller cone be r cm. Hence, the ratio of the volumes of the two parts will be 1 : 7.
Step-by-step explanation:
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