1. Surface Area of Pyramids and Cones
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Find the area of each regular polygon or circle.
1. Hexagon, radius 8 cm
ANSWER
cm2
2. Circle, radius 4 in.
ANSWER
50.27 in.2
3. Inscribed pentagon, radius 1 yd
ANSWER
2.38 yd2

3. Warm-Up
4. Find the perimeter of an inscribed square with radius 1 ft.
ANSWER
5.66 ft
5. Find the circumference of a circle with diameter 12.8 in.
ANSWER
40.21 in.

4. Use the Pythagorean Theorem to find the slant height l.
Example 1
A regular square pyramid has a height of 15 centimeters and a base edge length of 16 centimeters. Find the area of each lateral face of the pyramid.
SOLUTION
Use the Pythagorean Theorem to find the slant height l.
l2 = h2 +( b)2 1 2
Write formula.
Substitute for h and b. 1 2
l2 =
l2 = 289
Simplify.
l = 17
Find the positive square root.

5. Example 1
A = bl = (16)(17) = 136 square centimeters. 1 2
The area of each triangular face is

6. Example 2
Find the surface area and lateral area of the regular hexagonal pyramid.
SOLUTION
First, find the area of the base using the formula for
the area of a regular polygon, aP. The apothem a of
the hexagon is 5√ 3 feet and the perimeter P is =
60 feet. So, the area of the base B is (5√ 3)(60)
= 150√ 3 square feet. Then, find the surface area. 1 2

7. Example 2 1 S = B + Pl 2 1 = 150√ 3 + (60)(14) 2 = 150√ 3 + 420
Formula for surface area of regular pyramid.
= 150√ (60)(14) 1 2
Substitute known values.
= 150√
Simplify. ≈
Use a calculator.
The surface area of the regular hexagonal pyramid is about ft2. The lateral area is 420 ft2.

8. Guided Practice
1. Find the area of each lateral face of the regular pentagonal pyramid shown.
ANSWER
29.2 m2
2. Find the surface area of the regular pentagonal
pyramid shown.
256 m2
ANSWER

9. Example 3
SOLUTION
To find the slant height l of the right cone, use the Pythagorean Theorem.
l2 = h2+ r 2
Write formula.
l2 =
Substitute.
l = 10
Find positive square root.

10. Use the formula for the surface area of a right cone.
Example 3
Use the formula for the surface area of a right cone.
S = πr2 + πrl
Formula for surface area of a right
cone
= π(62) + π(6)(10)
Substitute.
= 96π
Simplify.
The correct answer is B.
ANSWER

11. Example 4
The traffic cone can be approximated by a right cone with radius 5.7 inches and height 18 inches. Find the approximate lateral area of the traffic cone.
TRAFFIC CONE
SOLUTION
To find the slant height l, use the Pythagorean Theorem.
l2 = (5.7)2, so l ≈ inches.

12. The lateral area of the traffic cone is about 338.4 square inches.
Example 4
Find the lateral area.
Lateral area = πrl
Write formula.
= π(5.7)(18.9)
Substitute known values. ≈
Simplify and use a calculator.
The lateral area of the traffic cone is about square inches.

13. Guided Practice
3. Find the lateral area of the right cone shown.
1178 yd2
ANSWER
4. Find the surface area of the right cone shown.
1885 yd2
ANSWER

14. Lesson Quiz
1. Find the lateral area of the regular pyramid.
ANSWER
300 cm2

15. Lesson Quiz
2. Find the surface area of the cone. Round to
the nearest hundredth.
ANSWER
in.2

16. Lesson Quiz
3. A right cone has radius 8 m and surface area
224π m2. Find its slant height.
ANSWER
20 m