A cone has base area #363# #cm^2#. A parallel slice #5# #cm# from the vertex has area #25# #cm^2#. What is the height of the cone?
1 Answer
Height of cone
Explanation:
Consider the circle at the base of the cone. We are told that this has an area of
The area of circle is given by
Hence the radius of the circle at the base
Now consider the circle formed by the parallel slice through the cone
Finally consider a vertical slice through the vertex of the cone perpendicular to the base. This has height (h), the height of the cone, and forms two similar triangles, one with sides h and the radius of the base
Since these triangles are similar, their corresponding sides are proportional. Hence:
Substituting for