SOLUTION: How to find d in simplest radical form in a right circular cone shape that has a radius of 3 and height of 3 and letter d outside the cone. Thanks in advance. a. sq root 6 b.

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Question 473275: How to find d in simplest radical form in a right circular cone shape that has a radius of 3 and height of 3 and letter d outside the cone. Thanks in advance.
a. sq root 6
b. 3 sq root of 2
c. 18
d. 6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you take a cross section of the cone, and you cut that cross section in half, you'll get the picture




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%5E2%2Bb%5E2=c%5E2 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%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


3%5E2%2B3%5E2=x%5E2 Plug in a=3, b=3, c=x


9%2B3%5E2=x%5E2 Square 3 to get 9.


9%2B9=x%5E2 Square 3 to get 9.


18=x%5E2 Combine like terms.


x%5E2=18 Rearrange the equation.


x=sqrt%2818%29 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%2Asqrt%282%29 Simplify the square root.


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Answer:


So the solution is x=3%2Asqrt%282%29, which means that the answer is choice B)