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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.
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 , where "r" is the radius of the cone.
The lateral area of a cone is , where L is the slant height.
Hence, for our problem we have this equation
= .
Divide both sides by to get
r = 3.
ANSWER. The radius of the base of this cone is 3 inches.
Solved (correctly and in a right way).