Question 1198591
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The total surface area of a right circular cone is one and one-half times the lateral area. 
The radius of the base is equal to _______inches if the slant height is 6 inches.
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        The solution by @MathLover1 is totally wrong,

        so I came to bring a correct solution.



<pre>
The problem says that "The total surface area of a right circular cone 
is one and one-half times the lateral area."


It means that the base area of the cone is half of its lateral area.


The base area of the cone is  {{{pi*r^2}}},  where "r" is the radius of the cone.

The lateral area of a cone is  {{{pi*r*L}}},  where L is the slant height.


Hence, for our problem we have this equation 

    {{{pi*r^2}}} = {{{(1/2)*pi*r*6}}}.


Divide both sides by  {{{pi*r}}}  to get

    r = 3.


<U>ANSWER</U>.  The radius of the base of this cone is 3 inches.
</pre>

Solved (correctly and in a right way).