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:

$$\begin{gathered} r=10\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r^2\cdot h \\ r:h=2r:2h \\ {V}_2=\frac{1}{3}\cdot \pi \cdot (2r{)}^2\cdot 2h \\ x=V_1:(V_2-V_1) \\ x=\frac{\pi \cdot r^2\cdot h}{\pi \cdot (2r{)}^2\cdot 2h-\pi \cdot r^2\cdot h} \\ x=\frac{r^2}{4r^2\cdot 2-r^2} \\ x=\frac{1}{4\cdot 2-1}=\frac{1}{7}\approx 0.1429=1:7 \end{gathered}$$

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