Homework
Geometry & Probability 8
Unit 1 – Volume & Surface Area
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Lesson 9 – Surface Area of Cones
The lateral area L.A. of a cone is π times the radius times the slant height, or L.A. = πrℓ.
The total surface area of a cone with slant height ℓ and radius r is the lateral area plus the area of the base, or
2
2
S.A. = L.A. + πr or S.A. = πrℓ + πr .
Example
Find the lateral and total surface areas of the cone. Round to the nearest tenth.
Lateral Surface Area
L.A. = πrℓ
L.A. = π • 3 • 5 r = 3, ℓ = 5
L.A. ≈ 47.1
Total Surface Area
The lateral and total surface areas of the cone are about 47.1 and 75.4 square centimeters.
Exercises
Find the lateral and total surface area of each cone. Use the pi key on your calculator. Show
your work. Round to the nearest hundredth.
1. LA = _________________
3. LA = _________________
2. SA = _________________
4. SA =_________________
5. _________________
Audrey uses a metal scoop to measure the correct amount of food to give to her horse. The scoop is
shaped like a cone with a diameter of 6 inches and a slant height of 8.5 inches. What is the lateral area
of the cone?
Formula: