A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its
axis and parallel to its base. Compare the volumes of the two parts.
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Answer:
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Answer:
The \: radius \: of \: upper \: cone (R _{1}) = \frac{4}{2 } = 2Theradiusofuppercone(R
1
)=
2
4
=2
Bottom radius 4cm
Volume \: of \: upper \: cone (V _{1}) = \frac{1}{3)} \pi r^{2} hVolumeofuppercone(V
1
)=
3)
1
πr
2
h
= \frac{1}{3} \pi \times ({2}^{2}) \times ( \frac{h}{2} )=
3
1
π×(2
2
)×(
2
h
)
Vol \: of \: bottom \: frustum (V_{2}) = \frac{\pi h}{3} (R \frac{2}{1} R \frac{2}{2} + R _{1}R _{2})Volofbottomfrustum(V
2
)=
3
πh
(R
1
2
R
2
2
+R
1
R
2
)
= \frac{\pi( \frac{h}{2}) }{3} (28)=
3
π(
2
h
)
(28)
Vol \: of \: bottom \: frustum (V _{2}) = \frac{\pi h}{6} (28)Volofbottomfrustum(V
2
)=
6
πh
(28)
\frac{V _{1} }{ V_{2} } = \frac{2\pi h}{3} \times \frac{6}{\pi h \times 28}
V
2
V
1
=
3
2πh
×
πh×28
6
\frac{V _{1}}{V _{2}} = \frac{2\pi h}{3} \times \frac{6}{\pi h \times 28}
V
2
V
1
=
3
2πh
×
πh×28
6
\frac{V_{1} }{ V_{2} } = \frac{1}{7}
V
2
V
1
=
7
1
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