(8) Lesson 8.5

1. Course 3, Lesson 8-5
Find the surface area of each cylinder. Round to the nearest
tenth.
1. 2.
3. 4.
5. A cylindrical storage tank will be painted. The tank has a height
of 58 feet and a radius of 4 feet. How much paint will be needed
to cover the surface?

2. Course 3, Lesson 8-5
ANSWERS
1. 427.3 cm2
2. 51.5 m2
3. 653.5 in2
4. 2,035.8 cm2
5. 1,558.2 ft2

3. WHY are formulas important
in math and science?
Geometry
Course 3, Lesson 8-5

4. Course 3, Lesson 8-5 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Geometry
• Extension of 8.G.9
Know the formulas for the volumes of cones, cylinders, and spheres
and use them to solve real-world and mathematical problems.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
7 Look for and make use of structure.

5. To
• find the lateral and total surface
area of a cone
Course 3, Lesson 8-5
Geometry

6. Course 3, Lesson 8-5
Geometry
Words The lateral area L.A. of a cone is π times the radius times the
slant height .
Symbols L.A. = πr
Model

7. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find the lateral area of the cone. Round to the nearest tenth.
L.A. = πrℓ
The lateral area of the cone is about 204.2 square millimeters.
Lateral area of a cone
L.A. = π • 5 • 13 Replace r with 5 and ℓ with 13.
L.A. ≈ 204.2 Simplify

8. Answer
Need Another Example?
Find the lateral area of the cone. Round to the nearest tenth.
252.6 m2

9. Course 3, Lesson 8-5
Geometry
Words The surface area S.A. of a cone with slant height ℓ and radius r
is the lateral area plus the area of the base.
Symbols S.A. = L.A. + πr2 or S.A. = πr + πr2

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Find the surface area of the cone. Round to the nearest tenth.
S.A. = πrℓ + πr2
The surface area of the cone is about 230.0 square inches.
Surface area of a cone
S.A. = π • 6 • 6.2 + π • 62 Replace r with 6 and ℓ with 6.2.
S.A. ≈ 230.0 Simplify

11. Answer
Need Another Example?
Find the surface area of the cone. Round to the
nearest tenth.
175.9 cm2

12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. A tepee has a radius of 5 feet and a slant height of 12 feet.
Find the lateral area of the tepee. Round to the nearest tenth.
L.A. = πrℓ
The lateral area of the tepee is about 188.5 square feet.
Lateral area of a cone
L.A. = π • 5 • 12 Replace r with 5 and ℓ with 12.
L.A. ≈ 188.5 Simplify

13. Answer
Need Another Example?
Ali is making conical hats for the school play.
Each hat will have a slant height of 18 inches
and a radius of 3.5 inches. How much fabric will
be needed to cover the lateral surface of each
hat? Round to the nearest tenth.
197.9 in2

14. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-5
Geometry

15. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-5
Geometry
Sample answers:
• The formula is used to find the lateral area of a
cone.
• is used to find the surface area of a cone.
. .L rA
. .S r r A 2

16. Write the formula for the
lateral surface area of a cone.
What does each variable in
the formula represent?
Course 3, Lesson 8-5
Ratios and Proportional RelationshipsFunctionsGeometry