SOLUTION: 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.

Algebra ->  Volume -> SOLUTION: 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.      Log On


   

Question 1198591: 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.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Total surface area of a cone =+pi%2Ar%2A%28r%2Bsqrt%28r%5E2%2Bh%5E2%29%29
Lateral surface area of a cone = +pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29
The total surface area of a right circular cone is one and one-half times the lateral area.
one and one-half=>3%2F2

.........simplify
r%2A+sqrt%28h%5E2+%2B+r%5E2%29+=+2+r%5E2.......if +h=6
r+%2Asqrt%2836+%2B+r%5E2%29+=+2r%5E2...........simplify
sqrt%2836+%2B+r%5E2%29+=+2r........square both sides
36+%2B+r%5E2+=+4r%5E2
36+=+4r%5E2-r%5E2+
3r%5E2+=36
r%5E2+=12
r=sqrt%2812%29
r≈3.464 inches

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~


        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  pi%2Ar%5E2,  where "r" is the radius of the cone.

The lateral area of a cone is  pi%2Ar%2AL,  where L is the slant height.


Hence, for our problem we have this equation 

    pi%2Ar%5E2 = %281%2F2%29%2Api%2Ar%2A6.


Divide both sides by  pi%2Ar  to get

    r = 3.


ANSWER.  The radius of the base of this cone is 3 inches.

Solved (correctly and in a right way).