Question 473275
If you take a cross section of the cone, and you cut that cross section in half, you'll get the picture



{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,3),
locate(1,-0.2,3),
locate(1,2,x)
)}}}


Note: Imagine spinning this triangle about the left side (as if it were a pole lodged in the ground). Doing so will generate the cone.




To find the unknown length x, we need to use the Pythagorean Theorem.



Remember, the Pythagorean Theorem is {{{a^2+b^2=c^2}}} where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.



Since the legs are {{{3}}} and {{{3}}} this means that {{{a=3}}} and {{{b=3}}}


   

Also, since the hypotenuse is {{{x}}}, this means that {{{c=x}}}.



{{{a^2+b^2=c^2}}} Start with the Pythagorean theorem.



{{{3^2+3^2=x^2}}} Plug in {{{a=3}}}, {{{b=3}}}, {{{c=x}}} 



{{{9+3^2=x^2}}} Square {{{3}}} to get {{{9}}}.



{{{9+9=x^2}}} Square {{{3}}} to get {{{9}}}.



{{{18=x^2}}} Combine like terms.



{{{x^2=18}}} Rearrange the equation.



{{{x=sqrt(18)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).



{{{x=3*sqrt(2)}}} Simplify the square root.



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Answer:



So the solution is {{{x=3*sqrt(2)}}}, which means that the answer is choice B)