A cone has a height of #16 cm# and its base has a radius of #8 cm#. If the cone is horizontally cut into two segments #7 cm# from the base, what would the surface area of the bottom segment be?
1 Answer
Explanation:
By cutting off a segment of a cone parallel to the base, you create what is known as a frustum. There are four important pieces of information in a fustrum: The height
By looking at the question, we see the original cone has a height of 16cm and a radius of 8cm. This means the relationship between the height and the radius is equal to
By cross multiplying, we find that
Finally we divide both sides by 16, to get
Now we have the value of
By looking at the image below, you should get an understanding of how this works using Pythagoras' Theorem.
http://www.ditutor.com/solid_gometry/frustum_cone.html
Now we simply plug in the values we have, to get
Now we know
http://www.ditutor.com/solid_gometry/frustum_cone.html
Where the bottom circle has the larger radius, and the top circle has the smaller radius.
We have all the values needed to solve this question, so lets plug them in to get
Therefor the surface area of the bottom segment of the cone is 528.233
I hope I helped!