F. Surface Area Explored - Right Cone

Another type of three-dimensional object is the right cone.

Right Cone

How is the lateral surface area portion of the formula generated?

The net of the lateral face is a partial circle.

Lateral face a side of any three-dimensional object that is not designated as a base

The arc length of the lateral face is equivalent to the circumference of the circular base with radius r. Assuming the lateral face is a whole circle, it will have a radius s, an area of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«msup»«mi mathvariant=¨normal¨»s«/mi»«mn»2«/mn»«/msup»«/math» and a circumference of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#960;«/mi»«mi mathvariant=¨normal¨»s«/mi»«/math». The area of the lateral face, relative to the area of the circular base, can then be determined using a proportion.

Arc length part of the circumference of the circle