Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.

Result

V1 =  0.185 l
V2 =  4.815 l

Solution:

V=5 l=5 1 dm3=5 dm3  V=13 S h  h1=13h S1=132S=19S  V1=13 S1 h1=13 19S 13h  V1=V 133=5 1335270.18520.185 lV=5 \ l=5 \cdot \ 1 \ dm^3=5 \ dm^3 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h \ \\ \ \\ h_{1}=\dfrac{ 1 }{ 3 } h \ \\ S_{1}=\dfrac{ 1 }{ 3^2 } S=\dfrac{ 1 }{ 9 } S \ \\ \ \\ V_{1}=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h_{1}=\dfrac{ 1 }{ 3 } \cdot \ \dfrac{ 1 }{ 9 } S \cdot \ \dfrac{ 1 }{ 3 } h \ \\ \ \\ V_{1}=V \cdot \ \dfrac{ 1 }{ 3^3 }=5 \cdot \ \dfrac{ 1 }{ 3^3 } \doteq \dfrac{ 5 }{ 27 } \doteq 0.1852 \doteq 0.185 \ \text{l}
V2=VV1=50.1852=963200=4.815 lV_{2}=V-V_{1}=5-0.1852=\dfrac{ 963 }{ 200 }=4.815 \ \text{l}



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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
#
Dr Math
1:3 is the ratio of heights
1:32 = 1:9 is the ratio of the area of base circles... due to two dimensional nature of the area.
1:33 = 1:27 is the ratio of volumes...  .. volume has three-dimensional nature

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