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valeera
The square root of 73. Since the theorem is a^2+b^2=c^2 and only works with right triangles. You take 2/2 the base so you have a right triangles with a hypotenuse if 9 and a side of 3. Then you just plug in to solve.
jcherry99
Step One
Find the radius of the cone. 
d = 6 which is given.
r = d/2
r = 6/2
r = 3

Remark
That's one of the sides of a right triangle. The other side is the slant of 9 inches. This is the hypotenuse.

Step Two
Find the height
h = ??
r = 3
Slant = 9

Use the Pythagorean theorem.

h^2 + r^2 = s^2
h^2 + 3^2 = 9^2
h^2 + 9 = 81  subtract 9 from both sides.
h^2 = 81 - 9
h^2 = 72
h = sqrt(72)

Step three
Express the answer
h = sqrt(72)
h = 8.49   <<<<<< Answer, but see below.

If you need this as a square root, then factor 72
72 = 6*6*2

h = sqrt(6* 6 * 2) The rule for square roots is if you have 2 of them you can take one outside the square root sign and throw the other one away.

h = 6 * sqrt(2) <<<< Answer

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