question_answer

From a circular sheet of paper of radius 10 cm, a sector of area 40% is removed. If the remaining part is used to make a conical surface, then the ratio of  the radius and the height of the cone is

A) 1 : 2

B) 1 : 1 

C) 3 : 4

D) 4 : 3

Correct Answer: C

Solution :

[c] Perimeter of circular sheet \[=2\pi r=20\pi \,cm\] \[\therefore \]The perimeter of base of conical surface \[=20\pi \times \frac{100-40}{100}=12\pi \] \[\therefore \]Radius of base of conical surface \[=\frac{12\pi }{2\pi }=6\,cm\] and height of conical surface \[=\sqrt{{{10}^{2}}-{{6}^{2}}}=8\,cm\] \[\therefore \]Required ratio \[=6:8=3:4\]