The height of the solid cone above is 18 inches and the radius of the base is 8 inches. A cut parallel to the circular bas is made completely through the con so that one of the two results is smaller cone. If the radius of the base of the small cone is 2 inches. What is the height of the small cone, in inches?
If it's cut in half, then maybe the height of the smaller cone is half of that of the bigger one? Don't trust me. I just started this subject in school. But it's an idea.
One of the two results is a smaller cone.. would your theory still work?
yes.
To find the height of the small cone, we can use the concept of similarity of triangles.
Let's consider the ratio of the heights of the two cones.
The height ratio is the same as the radius ratio, since the two cones are similar:
(ratio of heights) = (ratio of radii)
Let the height of the small cone be h.
Given that the radius of the base of the small cone is 2 inches, and the radius of the base of the large cone is 8 inches, we have:
(h / 18) = (2 / 8)
To find the value of h, we can solve this proportion:
h / 18 = 2 / 8
To cross multiply, we have:
8h = 2 * 18
8h = 36
Divide both sides by 8:
h = 36 / 8
h = 4.5 inches
Therefore, the height of the small cone is 4.5 inches.