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:

$r = 10 \ \text{cm} \ \\ V_{1}\ = \ \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h \ \\ \ \\ r:h\ = 2r:2h \ \\ \ \\ V_{2}\ = \ \dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ (2r)^2 \cdot \ 2h \ \\ \ \\ x\ = \ V_{1}:(V_{2}-V_{1}) \ \\ x\ = \ \dfrac{ \pi \cdot \ r^2 \cdot \ h }{ \ \pi \cdot \ (2r)^2 \cdot \ 2h-\pi \cdot \ r^2 \cdot \ h } \ \\ x\ = \ \dfrac{ r^2 }{ \ 4r^2 \cdot \ 2-r^2\ } \ \\ \ \\ x = \dfrac{ 1 }{ 4 \cdot \ 2-1 }≈ 0.1429 = 1:7$

Try another example