Lesson OVERVIEW of LESSONS on Surface Area of CONES

OVERVIEW of LESSONS on Surface Area of Cones

Major notions related to the surface area of cones

Figure 1a. A cone

Figure 1b. Flattening of the             lateral surface of a cone

Figure 1c. Flattening and the net                             of the cone surface

Major formulas for calculating the surface area of cones

1.  The lateral surface area of a cone  is   =  ,      where    is the radius of the cone's base and    is the slant height. 2.  The total surface area of a cone  is   = + = + = *(  ),      where    is the lateral surface area of the cone and    is the cone's base area.

(1)       (2)

My lessons on surface area of cones in this site

Solved problems on surface area of cones

- Find the lateral surface area of a cone if the triangular axial section of the cone has the area   = 100 .                                      - Find the lateral surface area of a cone if the triangular axial section of the cone has the area   = 10 .

- Find the surface area of a combined solid body which comprises of two identical cones joined base to base,  if their common                    base radius is of  3 cm  and the height is of  4 cm  each.     - Find the surface area of a combined solid body which comprises of two identical cones joined base to base,  if their common           base radius is of  4 cm  and the height is of  3 cm  each.

- Find the lateral surface area of a body  (a truncated cone)  obtained from a cone with the base radius of  6 cm  and the                           height of  8 cm  after cutting off the part of the cone by the plane parallel to the base in a way that the cutting plane           bisects the height of the original cone.