question_answer

The height and the radius of the base of a right circular cone are 12 cm and 6 cm respectively. The radius of the circular cross-section of the cone cut by a plane parallel to its base at a distance of 3 cm from the base is

A) 4 cm                            

B) 5.5 cm

C) 4:5 cm 

D) 3.5 cm

Correct Answer: C

Solution :

\[\Delta ADF\] and \[\Delta ABG\] are similar, \[\therefore \]      \[\frac{AG}{AF}=\frac{BG}{DF}\] \[\Rightarrow \]   \[\frac{12}{9}=\frac{6}{DF}\] \[\Rightarrow \]   \[12\times DF=6\times 9\] \[\Rightarrow \]   \[DF=\frac{6\times 9}{12}\]             \[=~\,4.5\,cm\]