Answer:
2√10 or 6.32455
Explanation:
The height of the cone is the distance from the base of the cone to the apex (the top point of the cone). A cross section of the cone is a plane that intersects the cone and cuts through it in such a way that it creates a shape that is similar to the base of the cone. In this case, the cross section is parallel to the base of the cone and has a radius of 4.
To find the height of the cone, we can use the Pythagorean Theorem. Let h be the height of the cone. We have:
(radius of base)^2 + h^2 = (radius of cross section)^2 + (distance between base and cross section)^2
Plugging in the given values, we get:
6^2 + h^2 = 4^2 + 8^2
Solving for h, we find that the height of the cone is: h = sqrt(40) = 2*sqrt(10).