Answer:
h = √72 in
Explanation:
When looking at the triangle formed inside the cone we know we already have a value to replace c for in the Pythagorean Theorem
a² + b² = c²
a² + b² = 9²
Now in order to find a value for b, we just have to get the value for the base of the cone, 6 in, and divide it by two, since the base of the cone is twice of the size of the base of the triangle:
a² + 3² = 9²
Now, we just solve for a:
a² + 3² = 9²
a² + 9 = 81
a² = 72
a = √72
So the height of the cone is √72 in.
You can also substitute √72 for a in the equation to check your work:
a² + 3² = 9²
(√72)² + 3² = 9²
72 + 9 = 81
81 = 81 True!!
hope this helps! :)