A cone 4

A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts.

Correct answer:

x =  1:7

Step-by-step explanation:

r=10 cm V1 = 13 π r2 h  r:h =2r:2h  V2 = 13 π (2r)2 2h  x = V1:(V2V1) x = π r2 h π (2r)2 2hπ r2 h x = r2 4r2 2r2   x=14 210.1429=1:7r = 10 \ \text{cm} \ \\ V_{1}\ = \ \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h \ \\ \ \\ r:h\ = 2r:2h \ \\ \ \\ V_{2}\ = \ \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ (2r)^2 \cdot \ 2h \ \\ \ \\ x\ = \ V_{1}:(V_{2}-V_{1}) \ \\ x\ = \ \dfrac{ \pi \cdot \ r^2 \cdot \ h }{ \ \pi \cdot \ (2r)^2 \cdot \ 2h-\pi \cdot \ r^2 \cdot \ h } \ \\ x\ = \ \dfrac{ r^2 }{ \ 4r^2 \cdot \ 2-r^2\ } \ \\ \ \\ x = \dfrac{ 1 }{ 4 \cdot \ 2-1 }≈ 0.1429 = 1:7



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You need to know the following knowledge to solve this word math problem:

geometryarithmeticsolid geometrybasic operations and conceptsUnits of physical quantitiesGrade of the word problem

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