# 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:

$V = 5 \ l = 5 \cdot \ 1 \ dm^3 = 5 \ dm^3 \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ S \cdot \ h \ \\ \ \\ h_{ 1 } = \dfrac{ 1 }{ 3 } h \ \\ S_{ 1 } = \dfrac{ 1 }{ 3^2 } S = \dfrac{ 1 }{ 9 } S \ \\ \ \\ V_{ 1 } = \dfrac{ 1 }{ 3 } \cdot \ S_{ 1 } \cdot \ h_{ 1 } = \dfrac{ 1 }{ 3 } \cdot \ \dfrac{ 1 }{ 9 } S \cdot \ \dfrac{ 1 }{ 3 } h \ \\ \ \\ V_{ 1 } = V \cdot \ \dfrac{ 1 }{ 3^3 } = 5 \cdot \ \dfrac{ 1 }{ 3^3 } = \dfrac{ 5 }{ 27 } \doteq 0.1852 = 0.185 \ \text { l }$
$V_{ 2 } = V-V_{ 1 } = 5-0.1852 = \dfrac{ 963 }{ 200 } = 4.815 = 4.815 \ \text { l }$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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 ## Next similar math problems:

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