question_answer

A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone?

A) 4 : 1

B) 8 : 1

C) 2 : 1

D) 6 : 1

Correct Answer: B

Solution :

[b] Let the cone is divided into two parts by a line,             In \[\Delta AOB\]and \[\Delta ACD\]                         \[\Delta AOB\sim \Delta ACD\] \[\Delta AOB\sim \Delta ACD\] By basic proportionality theorem, \[CD=\frac{T}{2},\] since\[AC=\frac{h}{2}\] Required ratio \[=\frac{\frac{1}{3}\pi {{r}^{2}}h}{\frac{1}{3}\pi {{\left( \frac{r}{2} \right)}^{2}}\left( \frac{h}{2} \right)}=\frac{8}{1}\] \[\therefore \]      Ratio = 8 : 1