Example 2:

Find the lateral surface area of a right cone whose base is a circle of diameter 10 inches and whose altitude is 12 inches:

 

Solution:

A net for the cone's lateral surface is a sector of a circle.  The radius of that circle is the slant height of the cone, and we can find that by the Pythagorean Theorem:

The circumference of the base is the length of the sector that forms the net, and is 10π.  The circumference of the circle containing that sector is 26π, so the sector is 10/26 or 5/13 of its circle and is subtended by an angle of 5/13 of 360^o, or about 138.5^o:

Therefore, the area of the sector is 5/13 the area of the circle with radius 13 inches, or about 204.2 square inches.

toc | return to top | previous page | next page