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Q.

Three identical cones with base radius r  are placed on their bases so that each is touching the other two. Then what is the measure of radius of the circle drawn through their vertices?


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a

= r  

b

< r  

c

> r  

d

None of the above 

answer is C.

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Detailed Solution

Given are three identical cones with base radius r  .
Question ImageThe base of the cone is equal to the side of the triangle.
We have the side of each equilateral triangle as 2r.
The circumference of the circle will be similar to the circumcircle that is drawn through the vertices of the cones.
We know, for an equilateral triangle with side a, radius of circumcircle is given by a 3  
Its radius will be, = 2r 3 >r  
Thus the radius of the circle will be larger than r.
Therefore the correct option is 3.
 
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