Question 1129272
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From the condition, the slant height  R is 4 times the cone radius  r :

    R = 4r.              (1)


If {{{alpha}}} is the angle under the question, then the length of the arc of the sector is

    s = {{{R*alpha}}} = {{{(4r)*alpha}}}.    (2)

   
At the same time, this length "s" is the circumference of the base of the cone:

    s = {{{2*pi*r}}}.           (3)


Equating (2) and (3), you get

    {{{4r*alpha}}} = {{{2*pi*r}}}.


Canceling "r" in both sides, you get

    {{{alpha}}} = {{{(2*pi)/4}}} = {{{pi/2}}}.       <U>ANSWER</U>


<U>Answer</U>.  The angle under the question is  {{{pi/2}}}.
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Solved.