course 3 8-8 surface area of pyramids and cones 8-8 surface area of pyramids and cones course 3 warm...
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Course 3
8-8 Surface Area of Pyramids and Cones
8-8 Surface Area of Pyramids and Cones
Course 3
Warm Up
Problem of the Day
Lesson Presentation
Course 3
8-8 Surface Area of Pyramids and Cones
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
1186.9 cm2
Course 3
8-8 Surface Area of Pyramids and Cones
Problem of the DaySandy 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
Course 3
8-8 Surface Area of Pyramids and Cones
Learn to find the surface area of pyramids and cones.
Course 3
8-8 Surface Area of Pyramids and Cones
Vocabulary
slant heightregular pyramidright cone
Course 3
8-8 Surface Area of Pyramids and Cones
The slant height of a pyramid or cone is measured along its lateral surface.
In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base.
The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent.
Right cone
Regular Pyramid
Course 3
8-8 Surface Area of Pyramids and Cones
Course 3
8-8 Surface Area of Pyramids and Cones
Additional Example 1: Finding Surface AreaFind the surface area of each figure to the nearest tenth. Use 3.14 for .
B. S = r2 + rl
= 20.16 ft2
= (32) + (3)(6)
= 27 84.8 cm2
A. S = B + Pl12
= (2.4 • 2.4) + (9.6)(3)12
Course 3
8-8 Surface Area of Pyramids and Cones
Check It Out: Example 1
= (3 • 3) + (12)(5)12
B. S = r2 + rl
= 39 m2
= (72) + (7)(18)
= 175 549.5 ft2
5 m
3 m3 m
7 ft
18 ft
A. S = B + Pl12
Find the surface area of each figure to the nearest tenth. Use 3.14 for .
Course 3
8-8 Surface Area of Pyramids and Cones
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.
Course 3
8-8 Surface Area of Pyramids and Cones
Check It Out: Example 2
Original Dimensions Triple the Slant Height
Triple the Radius
S = r2 + rl
= (4.5)2 + (4.5)(2)
= 29.25in2 91.8 in2
S = r2 + r(3l)
= (4.5)2 + (4.5)(6)
= 47.25in2 148.4 in2
S = r)2 + r)l
= (13.5)2 + (13.5)(2)
= 209.25in2 657.0 in2
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.
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.
Course 3
8-8 Surface Area of Pyramids and Cones
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?
= (10)(26) 816.8 mm2
Pythagorean Theorem
Lateral surface areaL = rl
a2 + b2 = l2
102 + 242 = l2
l = 26 24 mm
Course 3
8-8 Surface Area of Pyramids and Cones
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?
= (4)(15) 188.4 in2
12 in. 9 in.
Pythagorean Theorema2 + b2 = l2
92 + 122 = l2
l = 15Lateral surface areaL = rl
Course 3
8-8 Surface Area of Pyramids and Cones
Lesson Quiz: Part I
Find the surface area of each figure to the nearest tenth. Use 3.14 for .
1. the triangular pyramid
2. the cone175.8 in2
6.2 m2
Course 3
8-8 Surface Area of Pyramids and Cones
3. Tell whether doubling the dimensions of a cone will double the surface area.
Lesson Quiz: Part II
It will more than double the surface area because you square the radius to find the area of the base.