1. 8-8 Surface Area of Pyramids and Cones Warm Up Problem of the Day
Lesson Presentation
Course 3

2. Warm Up
1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m. What is the surface area?
2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3.14 for .
2.48 m2
cm2

3. Problem of the Day
Sandy is building a model of a pyramid with a hexagonal base. If she uses a toothpick for each edge, how many toothpicks will she need? 12

4. Learn to find the surface area of pyramids and cones.

5. Vocabulary
slant height
regular pyramid
right cone

6. The slant height of a pyramid or cone is measured along its lateral surface.
Regular Pyramid
Right cone
The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent.
In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base.

8. Additional Example 1: Finding Surface Area
Find the surface area of each figure to the nearest tenth. Use 3.14 for p. 1 2
A. S = B Pl
= (2.4 • 2.4) (9.6)(3) 1 2
= ft2
B. S = pr2 + prl
= p(32) + p(3)(6)
= 27p  84.8 cm2

9. Check It Out: Example 1
Find the surface area of each figure to the nearest tenth. Use 3.14 for p.
5 m 1 2
A. S = B Pl
= (3 • 3) (12)(5) 1 2
3 m
= 39 m2
3 m
B. S = pr2 + prl
18 ft
= p(72) + p(7)(18)
7 ft
= 175p  ft2

10. Additional Example 2: Exploring the Effects of Changing Dimensions
A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.

11. Triple the Slant Height
Check It Out: Example 2
A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.
Original Dimensions
Triple the Slant Height
Triple the Radius
S = pr2 + prl
S = pr2 + pr(3l)
S = p(3r)2 + p(3r)l
= p(4.5)2 + p(4.5)(2)
= p(4.5)2 + p(4.5)(6)
= p(13.5)2 + p(13.5)(2)
= 29.25p in2  91.8 in2
= 47.25p in2  in2
= p in2  in2
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

12. Additional Example 3: Application
The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass?
a2 + b2 = l2
Pythagorean Theorem
= l2
l = 26
24 mm
L = prl
Lateral surface area
= p(10)(26)  mm2

13. Check It Out: Example 3
A large road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone?
a2 + b2 = l2
Pythagorean Theorem
= l2
12 in.
9 in.
l = 15
L = prl
Lateral surface area
= p(4)(15)  in2

14. Lesson Quiz: Part I
Find the surface area of each figure to the nearest tenth. Use 3.14 for p.
1. the triangular pyramid
2. the cone
6.2 m2
175.8 in2

15. Lesson Quiz: Part II
3. Tell whether doubling the dimensions of a cone will double the surface area.
It will more than double the surface area because you square the radius to find the area of the base.