Surface Area and Volume: Surface Area and Volume of Pyramids and Cones

Surface Area of a Cone

with radius r, height h and slant height l
Cone

 

As you saw when drawing the surfaces of a cone, one side of a cone is not a shape that we have a simple formula for its area.  Because of this, we will use a formula to find the surface area of a cone.

Surface area of a cone = πr² + πrl,
where r is the radius of the base and l  is the slant height.

There are two parts to this formula.  The ‘πr²’ is the area of the circular base, and the ‘πrl’ is the outside part.

If you know the dimensions of r and l, you can simply use this formula without drawing out the sides.

Example:
Find the area of a cone with a base with radius 5 cm and slant height of 12 cm.

SA = πr² + πrl
SA = π(5)² + π(5)(12)
SA = 25π + 60π
SA = 85π cm²