Post on 28-Dec-2015
Holt CA Course 1
10-5 Surface Area of Pyramids and Cones
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
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Holt CA Course 1
10-5 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
Holt CA Course 1
10-5 Surface Area of Pyramids and Cones
Extension of MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
California Standards
Holt CA Course 1
10-5 Surface Area of Pyramids and Cones
Vocabulary
slant heightregular pyramidright cone
Holt CA Course 1
10-5 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 vertex 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
Holt CA Course 1
10-5 Surface Area of Pyramids and Cones
Holt CA Course 1
10-5 Surface Area of Pyramids and Cones
Additional Example 1: Finding Surface AreaFind the surface area of the figure to the nearest tenth. Use 3.14 for .
= 20.16 ft2
S = B + Pl12
= (2.4 • 2.4) + (9.6)(3)12
Holt CA Course 1
10-5 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 .
Holt CA Course 1
10-5 Surface Area of Pyramids and ConesAdditional Example 2: Exploring the Effects of Changing
Dimensions A cone has diameter 8 in. and slant height 3 in. Explain whether tripling only the slant height would have the same effect on the surface area as tripling only the radius. Use 3.14 for .
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.
Holt CA Course 1
10-5 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 only the slant height would have the same effect on the surface area as tripling only the radius. Use the 3.14 for .
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.
Holt CA Course 1
10-5 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
Holt CA Course 1
10-5 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?
= (9)(15) 424.1 in2
12 in. 9 in.
Pythagorean Theorema2 + b2 = l2
92 + 122 = l2
l = 15Lateral surface areaL = rl
Holt CA Course 1
10-5 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
Holt CA Course 1
10-5 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.