Lesson 12-5

Example 1  Lateral Area of a Cone
COSTUMES  Ingrid is making a hat for a costume	
from vinyl material. The hat is a cone with a diameter
of 6 inches and a height of 9 inches. Find the
lateral area of the hat.
Explore	We are given the altitude and the diameter
of the base. We need to find the slant height
of the cone.

Plan	The radius of the base, height, and slant height 	
form a right triangle. Use the Pythagorean 
Theorem to solve for the slant height. Then use
the formula for the lateral area of a right circular 
cone. To make calculations easier, change the 
diameter to 6.5, so the radius is 0.5(6.5) or 3.25, 
and the height to 9.75.

Solve	Write an equation and solve for l.
	l2	= (3.25)2 + (9.75)2	Pythagorean Theorem
	l2	= 105.625	Simplify.
	l	= 	Take the square root of each side.

	Next, use the formula for the lateral area of a right circular cone.
L	= πrl	Lateral area of a cone
	≈ π(3.25)( )	r = 3.25, l = 
	≈ 104.9	Use a calculator.

	The lateral area is approximately 104.9 square inches.

Check	Use estimation to check the reasonableness of this result. The lateral area is approximately (3)(3)(10) or 90 square inches. After comparing the result to the estimate, it can be determined that the answer is reasonable.

Example 2  Surface Area of a Cone
Find the surface area of the cone.	
T = πrl + πr2	Surface area of a cone
	= π(8.5)(19) + π(8.5)2	r = 8.5, l = 19
	≈ 734.3	Use a calculator.

The surface area is approximately 734.3 square meters.